KR20130132558A - Single-position hall effect measurements - Google Patents

Abstract

The first position on the test sample and its The method of determining by means of a multi-point probe comprising four contact elements the distance Y between the electrical boundaries 34 is characterized in that the test sample at the first position is carried out by the four contact elements 20, 22, 24, 26. Contacting with, applying a magnetic field at the first location, performing first and second four point measurements to derive first and second resistance values, and first and second resistance values. Calculating a first resistance difference, performing third and fourth four point measurements to derive third and fourth resistance values, calculating a second resistance difference with the third and fourth resistance values, Defining a first relation that includes the first resistance difference, the second resistance difference, and a parameter representing a distance between the first position and the electrical boundary, and wherein the first and second resistances in the first relation Determining the distance using a difference.

Description

Single Position Hall Effect Measurement {SINGLE-POSITION HALL EFFECT MEASUREMENTS}

In semiconductor processing, the continuous down of critical dimensions Increasingly, characterizing material properties with down-scaling It became important and difficult. Sheet materials such as ultra-shallow bonding are widely used. Sheet resistance measurements have been developed for the study. In addition to the sheet resistance of the film material, sheet carrier density and mobility are also important properties, for example, in the performance of semiconductor devices in complementary metal oxide semiconductor (CMOS) transistors. However, most current measurement methods for determining sheet resistance, sheet carrier density, and sheet carrier mobility require special sample preparation or destructive machining of the sample. Some measurement methods also require multiple engagements between the probe and the test sample, impairing the efficiency of the method.

Thus, a fast, cheap, non-destructive method is desirable for characterizing sheet carrier density and sheet material mobility. There are several ways to use microscopic multi-point probes fabricated by silicon-based microfabrication techniques that can be used to measure sheet resistance. WO2007045246A1 has shown that sheet resistance, sheet carrier density, and hole mobility can be measured by performing Hall effect measurements using an in-line micro four-point probe. However, this method requires two different couplings between the two measurement points, the probe and the test sample, which can cause large measurement errors if the electrical properties of the sample across the sample are not ideally uniform during the test.

It is an object of the present invention to improve the accuracy of the determination of the electrical properties of a test sample and to reduce its determination time. In particular, it is an object of the present invention to improve the accuracy of the electrical property determination and to reduce the determination time which depends on the distance to the electrical boundary of the test sample. According to the invention, only one measuring point is required in the Hall effect measurement, ie between the probe and the test sample. This greatly reduces measurement time and allows more accurate electrical It will give you the result of the transfer characteristic.

The The objective is to determine the distance between a first location on an electrically conducting surface portion of a test sample and an electrical boundary of the electrically conductive surface portion; A first aspect of the invention is achieved by a method of determining by a multi-point probe comprising a second contact element, a third contact element, and a fourth contact element, each contact element being tested. Defining a contact point for establishing electrical contact with the sample, the method further comprising (ii) placing the test sample at the first contact element, the second at the first location on the electrically conductive surface portion; Contacting a contact element, said third contact element, and said fourth contact element, (i.ii) a main magnetic field component perpendicular to said electrically conductive surface portion in said first position; applying a magnetic field having a component, (i.iii) applying a first potential across the first and third contact elements to generate a first current in the surface portion at the first location (I.iv) measuring the first current through the first or third contact element, (iv) measuring a first voltage across the second and fourth contact elements, ( i.vi) calculating a first resistance value R _B based on the first current and the first voltage, (i.vii) applying a second potential across the second and fourth contact elements Generating a second current in said surface portion at said first position, (i.viii) measuring said second current through said second or said fourth contact element, (i.ix) said second first and second measuring a second voltage across the third contact element, (ix) a second resistance value (R _{B ')} on the basis of the second current and the second voltage a Under the step, (i.xi) calculating a first resistance difference (△ R _{BB ')} on the basis of a difference between the first resistance and the second resistance value, (i.xii) the first and the Applying a third potential across the second contact element to generate a third current at the surface portion at the first position; (i.xiii) the third current passing through the first or second contact element; Measuring, (i.xiv) measuring a third voltage across the third and fourth contact elements, (i.xv) a third resistance value R based on the third current and the third voltage _C ), (i.xvi) applying a fourth potential across the third and fourth contact elements to generate a fourth current in the surface portion at the first location, (i.xvii) Measuring the fourth current through the third or fourth contact element (i.xviii) measuring a fourth voltage across the first and second contact elements, (ix ix) calculating a fourth resistance value R _{C ′} based on the fourth current and the fourth voltage, and (i.xx) based on a difference between the third resistance value and the fourth resistance value. Calculating a second resistance difference ΔR _{CC ′} , or in the alternative, the multi-point probe includes a plurality of contact elements, each contact element establishing an electrical contact with the test sample. Define a contact point for said plurality of contact elements comprising said first contact element, said second contact element, said third contact element, said fourth contact element and at least one further contact element, i.xii ) To (i.xx) in the following steps, namely (ii.xii) defining a contact element of a first configuration of the plurality of contact elements, wherein the contact element of the first configuration is the first contact element, The second contact element, the third contact element, and the fourth contact element; (ii.xiii) defining a contact element of a second configuration of the plurality of contact elements, wherein the contact element of the second configuration is a fifth contact element, a sixth contact element, a seventh contact element, and an eighth contact element. At least one of the contact elements of the second configuration is a contact element of the one or more additional contact elements, (ii.xiv) the test at the first location on the electrically conductive surface portion Contacting a sample with the contact element of the contact element of the second configuration and simultaneously contacting the test sample with the contact element of the contact element of the first configuration, (ii.xv) the fifth and seventh contact elements Applying a third potential at both ends to generate a third current at the surface portion at the first position, (ii.xvi) passing through the fifth or seventh contact element Measuring the third current, (ii.xvii) measuring a third voltage across the sixth and eighth contact elements, (ii.xviii) based on the third current and the third voltage Calculating a third resistance value (R _{B , 2} ), (ii.xix) applying a fourth potential across the sixth and eighth contact elements to generate a fourth current in the surface portion at the first position; (Ii.xx) measuring the fourth current through the sixth or eighth contact element, (ii.xxi) measuring a fourth voltage across the fifth and seventh contact elements (ii.xxii) calculating a fourth resistance value R _{B ′ , 2} based on the fourth current and the fourth voltage, and (ii.xxiii) the third resistance value and the fourth resistance. Alternatives and steps (ii.xii) comprising the steps (i.xii) to (i.xx) above, replacing with calculating the second resistance difference ΔR _{BB ′, 2} based on the difference between the values. ) To (ii.xxiii) Alternatives include both (i.xxi) first, second, and third parameters representing the first resistance difference, the second resistance difference, and the distance between the first position and the electrical boundary, respectively. the method comprising: defining a first relational expression (f), and (i.xxii) the first and second resistance difference _{(△ R BB ', △ R} CC', △ R BB ', 2) in said first relation, each Determining the third parameter representing the distance y between the first position and the electrical boundary using the first and second parameters. .

)을 계산하는 단계, (iii.xxv) 상기 제3 저항값(R_{B ,2}) 및 상기 제4 저항값(R_{B' ,2})의 제2 저항 평균(

)을 계산하는 단계, 및 (iii.xxvi) 상기 제1 및 제4 접촉 요소 양단에 제5 전위를 인가하여 상기 제1 위치에서 상기 표면부에 제5 전류를 발생시키는 단계, (iii.xxvii) 상기 제1 또는 상기 제4 접촉 요소를 통과하는 상기 제5 전류를 측정하는 단계, (iii.xxviii) 상기 제2 및 제3 접촉 요소 양단의 제5 전압을 측정하는 단계, (iii.xxix) 상기 제5 전류 및 상기 제5 전압에 기초하여 제5 저항값(R_{A ,1})을 계산하는 단계, (iii.xxx) 상기 제2 및 제3 접촉 요소 양단에 제6 전위를 인가하여 상기 제1 위치에서 상기 표면부에 제6 전류를 발생시키는 단계, (iii.xxxi) 상기 제2 또는 상기 제3 접촉 요소를 통과하는 상기 제6 전류를 측정하는 단계, (iii.xxxii) 상기 제1 및 제4 접촉 요소 양단의 제6 전압을 측정하는 단계, (iii.xxxiii) 상기 제6 전류 및 상기 제6 전압에 기초하여 제6 저항값(R_{A' ,1})을 계산하는 단계, (iii.xxxiv) 상기 제5 저항값(R_{A ,1}) 및 상기 제6 저항값(R_{A' ,1})의 제3 저항 평균(

)을 계산하는 단계, (iii.xxxv) 상기 제5 및 제8 접촉 요소 양단에 제7 전위를 인가하여 상기 제1 위치에서 상기 표면부에 제7 전류를 발생시키는 단계, (iii.xxxvi) 상기 제5 또는 상기 제8 접촉 요소를 통과하는 상기 제7 전류를 측정하는 단계, (iii.xxxvii) 상기 제6 및 제7 접촉 요소 양단의 제7 전압을 측정하는 단계, (iii.xxxviii) 상기 제7 전류 및 상기 제7 전압에 기초하여 제7 저항값(R_{A ,2})을 계산하는 단계, (iii.xxxix) 상기 제6 및 제7 접촉 요소 양단에 제8 전위를 인가하여 상기 제1 위치에서 상기 표면부에 제8 전류를 발생시키는 단계, (iii.xl) 상기 제6 또는 상기 제7 접촉 요소를 통과하는 상기 제8 전류를 측정하는 단계, (iii.xli) 상기 제5 및 제8 접촉 요소 양단의 제8 전압을 측정하는 단계, (iii.xlii) 상기 제8 전류 및 상기 제8 전압에 기초하여 제8 저항값(R_{A' ,2})을 계산하는 단계, (iii.xliii) 상기 제7 저항값(R_{A ,2}) 및 상기 제8 저항값(R_{A' ,2})의 제4 저항 평균(

)을 계산하는 단계, (iii.xliv) 상기 제1 저항 평균(

), 상기 제3 저항 평균(

), 및 제1 의사 시트(pseudo sheet) 저항(R_{P ,1})을 각각 나타내는 제4, 제5, 및 제6 파라미터를 포함하는 제2 관계식을 정의하는 단계, (iii.xlv) 상기 제2 관계식에서 상기 제1 저항 평균(

) 및 상기 제3 저항 평균(

)을 각각 상기 제4 파라미터 및 상기 제5 파라미터로서 이용하여 상기 제1 의사 시트 저항(R_{P ,1})을 나타내는 상기 제6 파라미터를 결정하는 단계, (iii.xlvi) 상기 제2 저항 평균(

), 상기 제4 저항 평균(

), 및 제2 의사 시트 저항(R_{P ,2})을 각각 나타내는 제7, 제8, 및 제9 파라미터를 포함하는 제3 관계식을 정의하는 단계, (iii.xlvii) 상기 제3 관계식에서 상기 제2 저항 평균(

) 및 상기 제4 저항 평균(

)을 각각 상기 제7 파라미터 및 상기 제8 파라미터로서 이용하여 상기 제2 의사 시트 저항(R_{PP 2})을 나타내는 상기 제9 파라미터를 결정하는 단계, (iii.xlviii) 상기 제1 의사 시트 저항(R_{P ,1}), 상기 제2 의사 시트 저항(R_{P ,2}), 및 상기 제1 위치와 상기 전기적 경계 간의 거리를 각각 나타내는 제10, 제11, 및 제12 파라미터를 포함하는 제4 관계식(g_D)을 정의하는 단계, 및 (iii.xlix) 상기 제4 관계식(g_D)에서 상기 제1 및 제2 의사 시트 저항(R_{P ,1}, R_{P ,2})을 각각 상기 제10 및 제11 파라미터로서 이용하여 상기 제1 위치와 상기 전기적 경계 간의 추가 거리(y)를 나타내는 상기 제12 파라미터를 결정하는 단계를 더 포함할 수 있고, 또는 단계 (iii.xlix)를 대체하는 대안예에서는, 상기 제2 구성의 상기 접촉 요소는 상기 테스트 샘플의 상기 전기적으로 전도성인 표면부 상의 제1 위치와 상기 전기적으로 전도성인 표면부의 상기 전기적 경계 간의 추가 거리(y₂)를 나타내고, 상기 제1 관계식(f_D)은 상기 제1 위치와 상기 전기적 경계 간의 상기 추가 거리를 나타내는 제13 파라미터를 더 포함하고, 상기 제4 관계식(g_D)은 상기 제1 위치와 상기 전기적 경계 간의 상기 추가 거리를 나타내는 제14 파라미터를 더 포함하며, 상기 방법은 (iv.xlix) 상기 제4 관계식(g_D)에서 상기 제1 및 제2 의사 시트 저항(R_{P ,1}, R_{P ,2})을 각각 상기 제10 및 제11 파라미터로서 이용하여 상기 제1 위치와 상기 전기적 경계 간의 상기 거리(y) 및 상기 추가 거리(y₂)를 각각 나타내는 상기 제13 파라미터 및 상기 제14 파라미터를 동시에 결정하는 단계를 더 포함한다.First aspect of the invention and A method according to an alternative to replacing steps (i.xii) to (i.xx) includes (iii.xxiv) a first of the first resistance value R _B and the second resistance value R _{B ′} . Resistance average (

), (Iii.xxv) a second resistance average of the third resistance value R _{B , 2} and the fourth resistance value R _{B ′ , 2}

) And (iii.xxvi) applying a fifth potential across the first and fourth contact elements to generate a fifth current in the surface portion at the first location, (iii.xxvii) Measuring the fifth current through the first or fourth contact element, (iii.xxviii) measuring a fifth voltage across the second and third contact elements, (iii.xxix) the Calculating a fifth resistance value R _{A , 1} based on a fifth current and the fifth voltage, (iii.xxx) applying a sixth potential across the second and third contact elements to provide the first Generating a sixth current in the surface portion at a position (iii.xxxi) measuring the sixth current passing through the second or third contact element, (iii.xxxii) the first and the third measuring a sixth voltage across the four contact elements, (iii.xxxiii) a sixth resistance value (R _{a ', 1)} on the basis of said sixth current and said sixth voltage Under the third phase of the average resistance, (iii.xxxiv) and the fifth resistance (R _{A, 1),} and the sixth resistance (R _{A ', 1)} (

), (Iii.xxxv) applying a seventh potential across the fifth and eighth contact elements to generate a seventh current in the surface portion at the first location, (iii.xxxvi) the Measuring the seventh current through the fifth or eighth contact element, (iii.xxxvii) measuring a seventh voltage across the sixth and seventh contact elements, (iii.xxxviii) Calculating a seventh resistance value R _{A , 2} based on the seventh current and the seventh voltage, (iii.xxxix) applying an eighth potential across the sixth and seventh contact elements to the first position; Generating an eighth current in the surface portion at (iii.xl) measuring the eighth current through the sixth or seventh contact element, (iii.xli) the fifth and eighth Measuring an eighth voltage across the contact element; (iii.xlii) calculating an eighth resistance value R _{A ' , 2} based on the eighth current and the eighth voltage; (Iii.xliii) a fourth resistance average of the seventh resistance value R _{A , 2} and the eighth resistance value R _{A ′ , 2} ;

), (Iii.xliv) the first resistance average (

), The third resistance average (

) And defining a second relationship comprising fourth, fifth, and sixth parameters representing the _first pseudo sheet resistance R _{P , 1} , respectively, (iii.xlv) In the relation, the first resistance average (

) And the third resistance average (

) Is used as the fourth parameter and the fifth parameter, respectively _, to determine the sixth parameter representing the first pseudo sheet resistance R _{P , 1} , (iii.xlvi) the second resistance average (

), The fourth resistance average (

), And defining a third relationship comprising the seventh, eighth, and ninth parameters representing the second pseudo sheet resistance R _{P , 2} , respectively, (iii.xlvii) the third relationship in the third relationship. 2 resistance average (

) And the fourth resistance average (

Determining the ninth parameter representing the second pseudo sheet resistance R _{PP 2} using the seventh and eighth parameters, respectively, (iii.xlviii) the first pseudo sheet resistance R _{P , 1} ), a fourth relational g including tenth, eleventh, and twelfth parameters representing the second pseudo sheet resistance R _{P , 2} and the distance between the first position and the electrical boundary, respectively. _D ), and (iii.xlix) the first and second pseudo sheet resistances R _{P , 1} , R _{P , 2 in} the fourth relation (g _D ), respectively; Determining, using the parameter, the twelfth parameter indicative of an additional distance y between the first position and the electrical boundary, or in an alternative alternative to step (iii.xlix), The contact element of the second configuration is on the electrically conductive surface portion of the test sample. A thirteenth parameter representing an additional distance y ₂ between a first position and the electrical boundary of the electrically conductive surface portion, wherein the first relation f _D represents the additional distance between the first position and the electrical boundary; Wherein the fourth relation g _D further comprises a fourteenth parameter indicative of the additional distance between the first position and the electrical boundary, wherein the method comprises (iv.xlix) the fourth relation g _D ) the distance y between the first position and the electrical boundary using the first and second pseudo sheet resistances R _{P , 1} , R _{P , 2 as} the tenth and eleventh parameters, respectively; Simultaneously determining the thirteenth parameter and the fourteenth parameter representing the additional distance y ₂ ; .

In an alternative comprising the step (iii.xlix), the fourth relation may be equal to R _{P, 1} / R _{P, 2} = g _D (y), where R _{P , 1} is the first pseudo sheet Represents a resistance, R _{P , 2} represents the second pseudo sheet resistance, g _D represents a function comprising the distance y as a parameter, the function g _D defines a peak value at a specific distance, and the function g _D increases when the function of the distance is below the specified distance and decreases when the function of the distance is above the specific distance, and the method (iii.xlx) determines the distance and the specific distance. In comparison, the fourth relation may further include determining whether the additional distance y ₂ is less than or above the specific distance. The additional distance y ₂ determined in this way is typically more accurate than the distance y because it is derived from the resistance average instead of the resistance difference.

The additional distance may replace the distance for any purpose, for example to determine the electrical properties of the test sample.

)을 계산하는 단계, (v.xv) 상기 제5 및 제7 접촉 요소 양단에 제3 전위를 인가하여 상기 제1 위치에서 상기 표면부에 제3 전류를 발생시키는 단계, (x.xvi) 상기 제5 또는 상기 제7 접촉 요소를 통과하는 상기 제3 전류를 측정하는 단계, (x.xvii) 상기 제6 및 제8 접촉 요소 양단의 제3 전압을 측정하는 단계, (x.xviii) 상기 제3 전류 및 상기 제3 전압에 기초하여 제3 저항값(R_{B ,2})을 계산하는 단계, (v.xix) 상기 제6 및 제8 접촉 요소 양단에 제4 전위를 인가하여 상기 제1 위치에서 상기 표면부에 제4 전류를 발생시키는 단계, (v.xx) 상기 제6 또는 상기 제8 접촉 요소를 통과하는 상기 제4 전류를 측정하는 단계, (v.xxi) 상기 제5 및 제7 접촉 요소 양단의 제4 전압을 측정하는 단계, (v.xxii) 상기 제4 전류 및 상기 제4 전압에 기초하여 제4 저항값(R_{B' ,2})을 계산하는 단계, (v.xxv) 상기 제3 저항값(R_{B ,2}) 및 상기 제4 저항값(R_{B' ,2})의 제2 저항 평균(

)을 계산하는 단계, (v.xxvi) 상기 제1 및 제4 접촉 요소 양단에 제5 전위를 인가하여 상기 제1 위치에서 상기 표면부에 제5 전류를 발생시키는 단계, (v.xxvii) 상기 제1 또는 상기 제4 접촉 요소를 통과하는 상기 제5 전류를 측정하는 단계, (v.xxviii) 상기 제2 및 제3 접촉 요소 양단의 제5 전압을 측정하는 단계, (v.xxix) 상기 제5 전류 및 상기 제5 전압에 기초하여 제5 저항값(R_{A ,1})을 계산하는 단계, (v.xxx) 상기 제2 및 제3 접촉 요소 양단에 제6 전위를 인가하여 상기 제1 위치에서 상기 표면부에 제6 전류를 발생시키는 단계, (v.xxxi) 상기 제2 또는 상기 제3 접촉 요소를 통과하는 상기 제6 전류를 측정하는 단계, (v.xxxii) 상기 제1 및 제4 접촉 요소 양단의 제6 전압을 측정하는 단계, (v.xxxiii) 상기 제6 전류 및 상기 제6 전압에 기초하여 제6 저항값(R_{A' ,1})을 계산하는 단계, (v.xxxiv) 상기 제5 저항값(R_{A ,1}) 및 상기 제6 저항값(R_{A' ,1})의 제3 저항 평균(

)을 계산하는 단계, (v.xxxv) 상기 제5 및 제8 접촉 요소 양단에 제7 전위를 인가하여 상기 제1 위치에서 상기 표면부에 제7 전류를 발생시키는 단계, (v.xxxvi) 상기 제5 또는 상기 제8 접촉 요소를 통과하는 상기 제7 전류를 측정하는 단계, (v.xxxvii) 상기 제6 및 제7 접촉 요소 양단의 제7 전압을 측정하는 단계, (v.xxxviii) 상기 제7 전류 및 상기 제7 전압에 기초하여 제7 저항값(R_{A ,2})을 계산하는 단계, (v.xxxix) 상기 제6 및 제7 접촉 요소 양단에 제8 전위를 인가하여 상기 제1 위치에서 상기 표면부에 제8 전류를 발생시키는 단계, (v.xl) 상기 제6 또는 상기 제7 접촉 요소를 통과하는 상기 제8 전류를 측정하는 단계, (v.xli) 상기 제5 및 제8 접촉 요소 양단의 제8 전압을 측정하는 단계, (v.xlii) 상기 제8 전류 및 상기 제8 전압에 기초하여 제8 저항값(R_{A' ,2})을 계산하는 단계, (v.xliii) 상기 제7 저항값(R_{A ,2}) 및 상기 제8 저항값(R_{A' ,2})의 제4 저항 평균(

)을 계산하는 단계, (v.xliv) 상기 제1 저항 평균(

), 상기 제3 저항 평균(

), 및 제1 의사 시트 저항(R_{P ,1})을 각각 나타내는 제4, 제5, 및 제6 파라미터를 포함하는 제2 관계식을 정의하는 단계, (v.xlv) 상기 제2 관계식에서 상기 제1 저항 평균(

) 및 상기 제3 저항 평균(

)을 각각 상기 제4 파라미터 및 상기 제5 파라미터로서 이용하여 상기 제1 의사 시트 저항(R_{P ,1})을 나타내는 상기 제6 파라미터를 결정하는 단계, (v.xlvi) 상기 제2 저항 평균(

), 상기 제4 저항 평균(

), 및 제2 의사 시트 저항(R_{P ,2})을 각각 나타내는 제7, 제8, 및 제9 파라미터를 포함하는 제3 관계식을 정의하는 단계, (x.xlvii) 상기 제3 관계식에서 상기 제2 저항 평균(

) 및 상기 제4 저항 평균(

)을 각각 상기 제7 파라미터 및 상기 제8 파라미터로서 이용하여 상기 제2 의사 시트 저항(R_{P ,2})을 나타내는 상기 제9 파라미터를 결정하는 단계, (v.xlviii) 상기 제1 의사 시트 저항(R_{P ,1}), 상기 제2 의사 시트 저항(R_{P ,2}), 및 상기 제1 위치와 상기 전기적 경계 간의 거리를 각각 나타내는 제10, 제11, 및 제12 파라미터를 포함하는 제4 관계식(g_D)을 정의하는 단계, 및 (v.xlix) 상기 제4 관계식(g_D)에서 상기 제1 및 제2 의사 시트 저항(R_{P ,1}, R_{P ,2})을 각각 상기 제10 및 제11 파라미터로서 이용하여 상기 제1 위치와 상기 전기적 경계 간의 거리(y)의 값을 나타내는 상기 제12 파라미터를 결정하는 단계를 포함한다.The above object is achieved by a method of determining by a multi-point probe comprising a plurality of contact elements a distance between a first position on an electrically conductive surface portion of a test sample and an electrical boundary of the electrically conductive surface portion. Acquired Achieved in accordance with a second aspect of the invention, each contact element defines a contact point for establishing electrical contact with the test sample, the plurality of contact elements comprising a first contact element, a second contact element, a third contact An element, a fourth contact element and one or more additional contact elements, the method comprising: (vi) defining a contact element of a first configuration of the plurality of contact elements, wherein the contact element of the first configuration is the first element; A contact element, said second contact element, said third contact element, and said fourth contact element, (v.ii) defining a contact element of a second configuration of said plurality of contact elements-said second The contact element of the configuration consists of a fifth contact element, a sixth contact element, a seventh contact element, and an eighth contact element, wherein at least one contact element of the contact element of the second configuration is of the one or more additional contact elements. Contact element-, (v. iii-iv) contacting the test sample with the contact element of the contact element of the first and second configuration at the first position on the electrically conductive surface portion, (vv) the 적 기 miracle at the first position (V.vi) applying a first potential across the first and third contact elements so as to apply a magnetic field to the surface portion at the first position. Generating a first current, (v.vii) measuring the first current through the first or third contact element, (v.viii) a first across the second and fourth contact elements Measuring a voltage, (v.ix) calculating a first resistance value (R _B ) based on the first current and the first voltage, (vx) a second voltage across the second and fourth contact elements; Applying a second potential to generate a second current at the surface portion at the first position, (v.xi) measuring the second current through the second or fourth contact element, (v.xii) measuring a second voltage across the first and third contact elements, ( x.viii) calculating a second resistance value R _{B ′} based on the second current and the second voltage, (v. xiv) the first resistance value R _B and the second resistance value First resistance average of (R _{B '} )

), (V.xv) applying a third potential across the fifth and seventh contact elements to generate a third current at the surface portion at the first location, (x.xvi) Measuring the third current through the fifth or seventh contact element, (x.xvii) measuring a third voltage across the sixth and eighth contact elements, (x.xviii) Calculating a third resistance value R _{B , 2} based on a third current and the third voltage, (v.xix) applying a fourth potential across the sixth and eighth contact elements to the first position Generating a fourth current in the surface portion at (v.xx) measuring the fourth current passing through the sixth or eighth contact element, (v.xxi) the fifth and seventh Measuring a fourth voltage across the contact element, (v.xxii) calculating a fourth resistance value R _{B ′ , 2} based on the fourth current and the fourth voltage, (v.xxv) Prize The second resistance average of the third resistance value R _{B , 2} and the fourth resistance value R _{B ′ , 2} (

), (V.xxvi) applying a fifth potential across the first and fourth contact elements to generate a fifth current at the surface at the first location, (v.xxvii) Measuring the fifth current through the first or fourth contact element, (v.xxviii) measuring a fifth voltage across the second and third contact elements, (v.xxix) Calculating a fifth resistance value R _{A , 1} based on a fifth current and the fifth voltage (v.xxx) by applying a sixth potential across the second and third contact elements to the first position; Generating a sixth current in the surface portion at (v.xxxi) measuring the sixth current passing through the second or third contact element, (v.xxxii) the first and fourth Measuring a sixth voltage across the contact element, (v.xxxiii) calculating a sixth resistance value R _{A ′ , 1} based on the sixth current and the sixth voltage, (v.xxxiv) a third resistance average of the fifth resistance value R _{A , 1} and the sixth resistance value R _{A ′ , 1}

), (V.xxxv) applying a seventh potential across the fifth and eighth contact elements to generate a seventh current in the surface portion at the first location, (v.xxxvi) the Measuring the seventh current through the fifth or eighth contact element, (v.xxxvii) measuring a seventh voltage across the sixth and seventh contact elements, (v.xxxviii) Calculating a seventh resistance value R _{A , 2} based on a seventh current and the seventh voltage, (v.xxxix) applying an eighth potential across the sixth and seventh contact elements to the first position; Generating an eighth current in the surface portion at (v.xl) measuring the eighth current passing through the sixth or seventh contact element, (v. Xli) the fifth and eighth Measuring an eighth voltage across the contact element, (v.xlii) calculating an eighth resistance value R _{A ' , 2} based on the eighth current and the eighth voltage, ( v.xliii) a fourth resistance average of the seventh resistor value R _{A , 2} and the eighth resistor value R _{A ′ , 2} ;

), (V.xliv) the first resistance average (

), The third resistance average (

) And defining a second relationship comprising fourth, fifth, and sixth parameters representing the first pseudo sheet resistance R _{P , 1} , respectively, (v.xlv) the second relationship in the second relationship. 1 resistance average (

) And the third resistance average (

) Is used as the fourth parameter and the fifth parameter, respectively _, to determine the sixth parameter representing the first pseudo sheet resistance R _{P , 1} , (v.xlvi) the second resistance average (

), The fourth resistance average (

), And defining a third relationship comprising a seventh, eighth, and ninth parameters representing the second pseudo sheet resistance R _{P , 2} , respectively, (x.xlvii) the third relationship in the third relationship. 2 resistance average (

) And the fourth resistance average (

) Is used as the seventh parameter and the eighth parameter, respectively _, to determine the ninth parameter representing the second pseudo sheet resistance R _{P , 2} , (v.xlviii) the first pseudo sheet resistance ( R _{P , 1} ), a fourth relational expression including the tenth, eleventh, and twelfth parameters representing the second pseudo sheet resistance R _{P , 2} and the distance between the first position and the electrical boundary, respectively; g _D ), and (v.xlix) the first and second pseudo sheet resistances R _{P , 1} , R _{P , 2 in} the fourth relation (g _D ), respectively; Determining the twelfth parameter representing a value of the distance y between the first position and the electrical boundary using as an eleventh parameter.

The fourth relation may be equal to R _{P , 1} / R _{P , 2} = g _D (y), where R _{P , 1} represents the first pseudo sheet resistance, and R _{P , 2} represents the second pseudo sheet Represents resistance, g _D represents a function comprising the distance y as a parameter, the function g _D defines a peak value at a certain distance, and the function g _D increases when the function of the distance is less than the specified distance and Decreasing when the function of the distance is greater than or equal to the specified distance, the method further comprising: (v.xlx) determining a distance representing an auxiliary distance by the method according to the first aspect of the invention, and (v xxlxi) may further include comparing the auxiliary distance with the specific distance and determining whether the distance is less than or greater than the specific distance in the fourth relational expression.

The method according to the first and second aspects of the present invention requires only one engagement between the probe and the test sample to accurately determine the distance.

Electrical boundaries prevent current from flowing out of the electrically conductive surface It should be understood as a boundary. Here, the relation is intended to encompass any suitable mathematical model of the setup used in the present method, including a single equation, a set of equations, a function, a set of functions, or specific parameters. It is intended. Determining the distance can include solving an equation, regression analysis, comparison with modeled or adjusted parameters, or any other mathematical technique suitable for a particular relationship.

The multi point probe may have any number of contact elements equal to or greater than four, for example the multi point probe may have twelve contact elements. However, four contact elements are employed regardless of the total number of contact elements. Contact elements not used in the method may be disposed between two contact elements used in the method. The multi-point probe can be a probe described in any of WO2010115771A1, WO2010000265A1, WO2008110174A1, WO2007051471A1, WO05124371A1, or WO0003252A2. The contact element may be in the form of a cantilevers extending from the probe body, for example as shown in WO0003252A2. The test sample may be a silicon wafer having a doped surface or thin metal film that defines an electrically conductive surface. The electrical boundary may be defined as part of the physical boundary of the electrically conductive surface portion, where the outside of the boundary is a non-conductive region. Alternatively, the electrical boundary may be defined as part of the physical boundary of the test sample as a whole when the electrically conductive surface portion extends to the physical boundary.

The magnetic field may be generated by an electromagnet or permanent magnet disposed on the opposite side of the test sample from the electrically conductive surface portion. The first, second, third, and fourth contact elements can be connected to a multiplexer, which in turn is a current source generating a potential across two of the contact elements, an ammeter for measuring current through the contact element, And a voltmeter measuring the voltage across two of said contact elements. A control unit can be connected to the multiplexer to automatically control the multiplexer to generate and measure current and to measure voltage as specified in the method.

The features described below can be used in both the first and second aspects of the invention.

The contact point may define a first line that intersects each of the contact points. The contact points of the first contact element, the second contact element, the third contact element, the fourth contact element, and the one or more additional contact elements may be associated with each of the contact points before the contact point contacts the test sample. An intersecting first line can be defined. The contact points of the first contact element, the second contact element, the third contact element, and the fourth contact element may be arranged in a predetermined order along the first line. The contact points of the fifth contact element, the sixth contact element, the seventh contact element, and the eighth contact element may be arranged in a predetermined order on the first line and / or along the first line. have.

The spacing between the first and second contact elements, the second and third contact elements, and the contact points of the third and fourth contact elements may be approximately equal to the first spacing value s ₁ . The spacing between the fifth and sixth contact elements, the sixth and seventh contact elements, and the contact points of the seventh and eighth contact elements may be approximately equal to the second interval value s ₂ .

Steps (i.xii) to (i.xx) In an alternative alternative, the first relationship may be equal to ΔR _{B B ′} / ΔR _{BB ′ , 2} = f _D (y, s ₁ , s ₂ ), where ΔR _{BB ′} is the first resistance DELTA R _BB'2 denotes the second resistance difference, and f _D denotes a distance y between the first position and the electrical boundary, the first interval value s ₁ , and the second interval value s ₂ . It is a function to include.

와 같을 수 있다.In the first relation ΔR _{BB ′} / ΔR _{BB ′ , 2} = f _D (y, s ₁ , s ₂ ), the function f _D (y, s ₁ , s ₂ ) is

≪ / RTI >

과 같을 수 있고, 여기서 R_{P , 1}는 상기 제1 의사 시트 저항이고,

는 상기 제1 저항 평균이고,

은 상기 제3 저항 평균이며, 상기 제3 관계식은

과 같을 수 있고, 여기서 R_{P ,2}는 상기 제2 의사 시트 저항이고,

는 상기 제2 저항 평균이며,

는 상기 제4 저항 평균이다.The second relation is

May be equal to, wherein R _{P , 1} is the first pseudo sheet resistance,

Is the first resistance average,

Is the third resistance average, and the third relational expression is

May be equal to, wherein R _{P , 2} is the second pseudo sheet resistance,

Is the second resistance average,

Is the fourth resistance average.

The contact point may define a first line that intersects each of the contact points, that is, the contact points are on a common line. have.

remind Containing steps (iii.xlix) In an alternative, the fourth relation may be equal to R _{P, 1} / R _{P, 2} = g _D (y, s ₁ , s ₂ ), where R _{P , 1} represents the first pseudo sheet resistance, R _{P , 2} represents the second pseudo sheet resistance, and g _D is a function comprising a distance y between the first position and the electrical boundary, the first spacing value s ₁ , and the second spacing value s ₂ . Indicates.

To replace step (iii.xlix) above Alternatively, the first relation may be equal to _{ΔR BB ′} / ΔR _{BB ′, 2} = f _D (y, y ₂ , s ₁ , s ₂ ), where ΔR _{BB ′} is the first resistor. ΔR _{BB '2} represents the second resistance difference, f _D is the distance y between the first position and the electrical boundary and the additional distance y ₂ , the first spacing value s ₁ , and the A function including a second interval value s ₂ .

와 같을 수 있다.The first relation _{△ R BB '/ △ R BB} ', 2 = f D (y, y 2, s 1, s 2) from the function _{f D (y, y 2,} s 1, s 2) is

≪ / RTI >

In an alternative to replacing step (iii.xlix), the fourth relation may be equal to R _{P, 1} / R _{P, 2} = g _D (y, y ₂ , s ₁ , s ₂ ), where R _{P , 1} represents the first pseudo sheet resistance, R _{P , 2} represents the second pseudo sheet resistance, g _D is the distance y between the first position and the electrical boundary and the additional distance y ₂ , the Represents a function comprising a first interval value s ₁ and the second interval value s ₂ .

The electrical boundary may have a substantially linear portion and on the first position and the linear portion The distance between one point may be shorter than the distance between the first location and any point on the electrical boundary outside the linear portion. This means that the shortest distance from the first position to the electrical boundary is to a point on the linear portion it means.

The method comprises (vi.i) placing the multi-point probe in the first line in a parallel relationship with the linear portion. Orienting may further comprise. The spacing between the first and second contact elements, the second and third contact elements, and the connection points of the third and fourth contact elements can be approximately equal.

In an alternative comprising the steps (i.xii) to (i.xx), the first relation may be equal to ΔR _{C C ′} / ΔR _{BB ′} = f (y, s), where ΔR _{BB '} represents the first resistance difference, ΔR _{C C'} represents the second resistance difference, f is the distance y between the first position and the electrical boundary and the distance s between the contact points as a parameter. It is a function to include.

와 같을 수 있고, 여기서 △R_BB'는 상기 추가적인 제1 저항차(△R_BB')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내고, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내며, 상기 관계식 △R_CC'/△R_BB'=f(y,s)에서 상기 제2 저항차 △R_CC'는

와 같을 수 있고, 여기서 △R_CC'는 상기 추가적인 제2 저항차(△R_CC')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타낸다.In the relation ΔR _{CC ′} / ΔR _{BB ′} = f (y, s), the first resistance difference ΔR _{BB ′} is

Wherein ΔR _{BB ′} represents the additional first resistance difference ΔR _{BB ′} , y represents the distance y, and a is between the contact points of the first and second contact elements. The interval, b denotes the interval between the contact points of the second and third contact element, c denotes the interval between the contact points of the third and fourth contact element, the relationship ΔR _{CC '} / ΔR _{BB '} = f (y, s), the second resistance difference ΔR _CC' is

ΔR _{CC ′} represents the additional second resistance difference ΔR _{CC ′} , y represents the distance y, and a is between the contact points of the first and second contact elements. B represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements.

Of one aspect of the present invention Comprising the steps (i.xii) to (i.xx) In an alternative, the method comprises (i.xxiii) applying a fifth potential across the first and fourth contact elements to generate a fifth current in the surface portion at the first location, (i.xxiv) Measuring the fifth current through the first or fourth contact element, (i.xxv) measuring a fifth voltage across the second and third contact elements, (i.xxvi) Calculating a fifth resistance value R _A based on a fifth current and the fifth voltage, (i.xxvii) applying a sixth potential across the second and third contact elements at the first position Generating a sixth current in the surface portion, (i.xxviii) measuring the sixth current passing through the second or third contact element, (i.xxix) the first and fourth contacts Measuring a sixth voltage across the element, (i.xxx) calculating a sixth resistance value R _{A '} based on the sixth current and the sixth voltage, ( i.xxxi) calculating a third resistance difference ΔR _{AA ′} based on the difference between the fifth resistance value and the sixth resistance value, (i.xxxii) defining the first relation f; In this case, a fourth parameter representing the third resistance difference ΔR _{AA ′} is further included in the first relation f. And (i.xxxiii) the first and the second, which may be used as first and second parameters in the first relation, respectively, when determining the distance y between the first position and the electrical boundary. The method may further include using the third resistance difference ΔR _{AA ′} as the fourth parameter in addition to the resistance differences _{ΔR BB ′} and ΔR _{CC ′} .

This allows for accurate measurement of the distance y using an asymmetric probe with a non-equidistant contact point.

The contact points can be arranged in line, and the spacing between the contact points of the first and second contact elements and the spacing between the contact points of the second and third contact elements can be approximately equal. The contact points may be arranged in line, and the spacing between the contact points of the third and fourth contact elements may be different from the spacing between the contact points of the first and second contact elements. In simulations, this particular relative spacing of contact probes allows for accurate determination of the distance to the electrical boundary. I knew that.

The spacing between the contact points of the third and fourth contact elements is in the range 1.1-3.7, 1.2-3.3, 1.3-2.9, 1.4-2.5, 1.5-2.1, and more than the spacing between the contact points of the first and second contact elements. One or more of 1.6-1.7, and / or range 1.2-1.3, 1.3-1.4, 1.4-1.5, 1.5-1.6, 1.6-1.7, 1.7-1.8, 1.8-1.9, 1.9-2.0, 2.0-2.2, 2.2-2.4 , Factor within one of 2.4-2.6, 2.6-2.8, 2.8-3.0, 3.0-3.3, 3.3-3.6, 3.6-3.9, and / or approximately 5 divided by 3, or one or more of the ranges 1.2-3.8, 1.6-3.4, 1.8-3.2, 2.0-3.0, 2.2-2.8, and 2.4-2.6, and / or 1.2-1.3, 1.3-1.4, 1.4 -1.5, 1.5-1.6, 1.6-1.7, 1.7-1.8, 1.8-1.9, 1.9-2.0, 2.0-2.2, 2.2-2.4, 2.4-2.6, 2.6-2.8, 2.8-3.0, 3.0-3.3, 3.3-3.6 , Factor within one of 3.6-3.9, and / or approximately five divided by two. In the simulation, this particular relationship gives the exact distance to the electrical boundary. I knew it made me decide.

The spacing between the contact points of the first and second contact elements can range from 1-5 μm, 5-10 μm, 10-15 μm, 15-20 μm, 20-25 μm, 25-30 μm, 30-40 μm, One of 40-50 μm, 50-500 μm, and / or within one or more of the ranges 1-50 μm, 5-40 μm, 10-30 μm, 15-25 μm.

The first relation may be equal to (ΔR _{AA ′} + αΔR _{CC ′} ) / ΔR _{BB ′} = f (y, a, b, c), where ΔR _{BB ′} is the first resistance difference, ΔR _{CC '} is the second resistance difference, ΔR _AA' is the third resistance difference, α is a tuning factor in the range from -10 to 10, and f is the electrical boundary with the first position. Is a function including the distance y between, a represents the spacing between the contact points of the first and second contact elements, b represents the spacing between the contact points of the second and third contact elements, and c is the third And the spacing between the contact points of the fourth contact element.

The tuning factor α may be about 1 or about −1.

와 같을 수 있고, 여기서 △R_BB'는 상기 추가적인 제1 저항차(△R_AA')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내고, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내며, 상기 관계식 (△R_AA'+α△R_CC')/△R_BB'= f(y,a,b,c)에서 상기 제2 저항차 △R_CC'는

와 같을 수 있고, 여기서 △R_CC'는 상기 추가적인 제2 저항차(△R_CC')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내고, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내며, 상기 관계식 (△R_AA'+α△R_CC')/△R_BB'= f(y,a,b,c)에서 상기 제3 저항차 △R_AA'는

와 같을 수 있고, 여기서 △R_AA'는 상기 추가적인 제3 저항차 (△R_AA')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 상기 간격을 나타낸다. 이러한 특정 모델링은 광범위한 측정 조건에 대해 정확한 결과를 낳는다는 것을 알았다.In the relation (ΔR _{AA ′} + αΔR _{CC ′} ) / ΔR _{BB ′} = f (y, a, b, c), the first resistance difference ΔR _{BB ′} is

Wherein ΔR _{BB ′} represents the additional first resistance difference ΔR _{AA ′} , y represents the distance y, and a is between the contact points of the first and second contact elements. The interval, b denotes the interval between the contact points of the second and third contact elements, c denotes the interval between the contact points of the third and fourth contact elements, the relation (ΔR _{AA '} + αΔ At R _{CC '} ) / ΔR _BB' = f (y, a, b, c), the second resistance difference ΔR _{CC '} is

ΔR _{CC ′} represents the additional second resistance difference ΔR _{CC ′} , y represents the distance y, and a is between the contact points of the first and second contact elements. The interval, b denotes the interval between the contact points of the second and third contact elements, c denotes the interval between the contact points of the third and fourth contact elements, the relation (ΔR _{AA '} + αΔ At R _{CC '} ) / ΔR _BB' = f (y, a, b, c), the third resistance difference ΔR _{AA '} is

ΔR _{AA ′} represents the additional third resistance difference ΔR _{AA ′} , y represents the distance y, and a is between the contact points of the first and second contact elements. B represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements. It was found that this particular modeling produced accurate results over a wide range of measurement conditions.

The spacing between the contact points of the first and second contact elements is one or more of the range 0.1-100 μm, 1-90 μm, 10-80 μm, 20-70 μm, 30-60 μm, and 40-50 μm, and And / or range 0.1-1 μm, 1-10 μm, 10-20 μm, 20-30 μm, 30-40 μm, 40-50 μm, 50-60 μm, 60-70 μm, 70-80 μm, 80- It may be within one of 90 μm, 90-100 μm, or 100-500 μm.

The object of the invention is achieved by a method of determining electrical properties at a first location on an electrically conductive surface portion of a test sample according to a third aspect of the invention, the electrically conductive surface portion having an electrical boundary, The method according to any one of (a) features 1 to 32 Determining a distance y between the first location on the electrically conductive surface portion of the test sample and the electrical boundary of the electrically conductive surface portion, (b) determining the electrical property and the distance y Defining a fifth relation comprising a fifteenth parameter to indicate, and (c) determining said electrical property using said distance y as said fifteenth parameter in said fifth relation, or alternatively The method further comprises (a) an additional distance y between the first position on the electrically conductive surface portion of the test sample according to any one of features 2 to 32 and the electrical boundary of the electrically conductive surface portion y ₂ ) determining, (b) defining a fifth relationship comprising a fifteenth parameter indicative of said electrical characteristic and said additional distance y ₂ , and (c ) Using the additional distance y ₂ as the fifteenth parameter in the fifth relation to determine the electrical property.

According to the method, there is only one time between the probe and the test sample to accurately determine the electrical characteristics. Only need to be combined.

Electrical boundaries are to be understood as boundaries that prevent current from flowing out of an electrically conductive surface. Here, a relation is intended to encompass any suitable mathematical model of the arrangement used in the method, including a single equation, a set of equations, a function, a set of functions, or a specific parameter. Determining the electrical properties described above may involve solving an equation, regression analysis, comparison with modeled or adjusted parameters, or any other mathematical technique suitable for a particular relationship.

The fifth relation may further comprise the spacing between the contact points of the first contact element, the second contact element, the third contact element, and / or the fourth contact element, (b ') the second When defining a fifth relationship, the fifth relationship further comprises a sixteenth parameter representing a distance between the contact points of the first contact element, the second contact element, the third contact element, and / or the fourth contact element. Can contain However, (c ') When determining the electrical property, the interval may be used as the sixteenth parameter in addition to the distance y or the additional distance y ₂ in the fifth relation.

The electrical property may be a Hall sheet resistance (R _H ), and the fifth relation (f ₁ , f ₂ ) further includes a seventeenth parameter representing an additional first resistance difference ΔR _{BB ′} . The method may comprise (d) applying an additional first potential across the first and third contact elements to generate an additional first current in the surface portion at the first location, (e) the second Measuring the additional first current through the first or third contact element, (f) measuring the additional first voltage across the second and fourth contact elements, (g) the additional first current And calculating the additional first resistance value R _B based on the additional first voltage, or (g ') determining the distance as the additional first resistance value R _B. the method comprising holding the (R _B), and (h) added to the two ends of the second and fourth contact elements Applying a second potential to generate an additional second current at the surface portion at the first location; (i) measuring the additional second current through the second or fourth contact element, (j) measuring an additional second voltage across the first and third contact elements, and (k) an additional second resistance value R _{B ′} based on the additional second current and the additional second voltage. Or (k ') retaining the second resistance value R _B' from determining the distance as an additional second resistance value R _{B '} , and (l) the additional agent Calculating the additional first resistance difference ΔR _{BB ′} based on the difference between the first resistance value and the additional second resistance value, or (l ′) the distance from the additional first resistance difference ΔR _BB. a step of holding a) _"), the first resistance difference (R _BB from the determining _in" the fabric .

와 같을 수 있고, 여기서 △R_{B B'}는 상기 추가적인 제1 저항차(△R_BB')를 나타내고, y는 상기 거리(y) 또는 추가 거리(y₁)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타낸다.The fifth relationship is

ΔR _{B B ′} represents the additional first resistance difference ΔR _{BB ′} , y represents the distance y or additional distance y ₁ , and a represents the first and Represents the spacing between the contact points of the second contact element, b represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements.

The electrical property may be a hole sheet resistance (R _H ), and the fifth relation (f ₂ , f ₃ ) may further include a seventeenth parameter representing an additional second resistance difference ΔR _{CC ′} . The method includes (d) applying an additional third potential across the first and second contact elements to generate an additional third current at the surface portion at the first location, (e) a phase first or second Measuring the additional third current through the second contact element, (f) measuring an additional third voltage across the third and fourth contact elements, and (g) the additional third current and the additional Calculating an additional third resistance value R _C based on the third voltage, Or the steps (i.xii) to (i.xx) In the alternative, (g ') the step of holding the third resistance value (R _C) from the step of determining the distance to an additional third resistance value (R _C), and (h) said third and fourth contact Applying an additional fourth potential across the element to generate an additional fourth current at the surface portion at the first location; (i) measuring the additional fourth current through the third or fourth contact element; (J) measuring an additional fourth voltage across the first and second contact elements, and (k) an additional fourth resistance value R based on the additional fourth current and the additional fourth voltage. _{C '} ), or comprising steps (i.xii) to (i.xx) above In an alternative, (k ') retaining the fourth resistance value R _C' from determining the distance as an additional fourth resistance value R _{C '} , and (l) the additional third resistance Calculating an additional second resistance difference ΔR _{CC ′} based on the difference between the value and the additional fourth resistance value, or in an alternative comprising the steps (i.xii) to (i.xx) , (l ') can further comprise the step of holding said second resistance difference (△ R _CC') from the step of determining in the second additional resistance difference (△ R _CC the distance _").

와 같을 수 있고, 여기서 △R_CC'는 상기 추가적인 제2 저항차(△R_CC')를 나타내고, y는 상기 거리(y) 또는 추가 거리(y₁)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내고, c는 상기 제3 및 제4 접촉 요소의 상기 접촉점들 간의 상기 간격을 나타낸다.The fifth relationship is

ΔR _{CC ′} represents the additional second resistance difference ΔR _{CC ′} , y represents the distance y or the additional distance y ₁ , and a represents the first and first Represents the spacing between the contact points of the second contact element, b represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements.

The electrical property may be a hole sheet resistance R _H , and the fifth relation f ₁ may further include a seventeenth parameter representing an additional third resistance difference ΔR _{AA ′} , and the method may include (d) applying an additional fifth potential across the first and fourth contact elements to generate an additional fifth current at the surface portion at the first location, (e) the first or fourth contact element Measuring the additional fifth current passing through (f) measuring an additional fifth voltage across the second and third contact elements, and (g) the additional fifth current and the additional fifth voltage based on the step of calculating the additional fifth resistance (R _a), or (g ') holding the fifth resistance (R _a) from the step of determining the distance to an additional fifth resistance (R _a) And (h) an additional sixth electrode across said second and third contact elements. Applying an upper side to generate an additional sixth current in the surface portion at the first position, (i) measuring the additional sixth current through the second or third contact element, (j) Measuring an additional sixth voltage across the first and fourth contact elements, and (k) calculating an additional sixth resistance value R _{A '} based on the additional sixth current and the additional sixth voltage. Or (k ') retaining the sixth resistance value R _A' from determining the distance as an additional fifth resistance value R _{A '} , and (l) the additional fifth resistance value Calculating the additional third resistance difference ΔR _{AA ′} based on the difference between the second resistance value and the additional sixth resistance value, or (l ′) converting the distance to the additional third resistance difference ΔR _{AA ′} . And retaining the third resistance difference ΔR _{AA ′} from the determining. have.

와 같을 수 있고, 여기서 △R_AA'는 상기 추가적인 제3 저항차(△R_AA')를 나타내고, y는 상기 거리(y) 또는 추가 거리(y₁)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타낸다.The fifth relationship is

ΔR _{AA ′} represents the additional third resistance difference ΔR _{AA ′} , y represents the distance y or the additional distance y ₁ , and a represents the first and the first Represents the spacing between the contact points of the second contact element, b represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements.

)을 계산하는 단계, 및 (d") 상기 제1 및 제3 접촉 요소 양단에 추가적인 제1 전위를 인가하여 상기 제1 위치에서 상기 표면부에 추가적인 제1 전류를 발생시키는 단계, (e") 상기 제1 또는 상기 제3 접촉 요소를 통과하는 상기 추가적인 제1 전류를 측정하는 단계, (f") 상기 제2 및 제4 접촉 요소 양단의 추가적인 제1 전압을 측정하는 단계, (g") 상기 추가적인 제1 전류 및 상기 추가적인 제1 전압에 기초하여 추가적인 제1 저항값(R_B)을 계산하는 단계, 또는 (g"') 상기 거리를 추가적인 제1 저항값(R_B)으로 결정하는 단계로부터 상기 제1 저항값(R_B)을 보유하는 단계, 및 (h") 상기 제2 및 제4 접촉 요소 양단에 추가적인 제2 전위를 인가하여 상기 제1 위치에서 상기 표면부에 추가적인 제2 전류를 발생시키는 단계, (i") 상기 제2 또는 상기 제4 접촉 요소를 통과하는 상기 추가적인 제2 전류를 측정하는 단계, (j") 상기 제1 및 제3 접촉 요소 양단의 추가적인 제2 전압을 측정하는 단계, (k") 상기 추가적인 제2 전류 및 상기 추가적인 제2 전압에 기초하여 추가적인 제2 저항값(R_B')을 계산하는 단계, 또는 (k''') 상기 거리를 추가적인 제2 저항값(R_B')으로 결정하는 단계로부터 상기 제2 저항값(R_B')을 보유하는 단계, 및 (l") 상기 추가적인 제1 저항값(R_B) 및 상기 추가적인 제2 저항값(R_B')의 제6 저항 평균(

)을 계산하는 단계, 및 (m) 상기 제5 저항 평균(

), 상기 제6 저항 평균(

), 및 상기 의사 시트 저항(R_P)을 각각 나타내는 제18, 제19, 및 제20 파라미터를 포함하는 제6 관계식을 정의하는 단계, (n) 상기 제6 관계식에서 상기 제5 저항 평균(

) 및 상기 제6 저항 평균(

)을 각각 상기 제18 파라미터 및 상기 제19 파라미터로서 이용하여 상기 의사 시트 저항(R_P)을 결정하는 단계를 더 포함할 수 있다.The electrical property may be sheet resistance R ₀ , and the fifth relation g may further include a seventeenth parameter representing a pseudo sheet resistance R _P , and the method may include (d ) Applying an additional fifth potential across the first and fourth contact elements to generate an additional fifth current at the surface portion at the first location, (e) passing through the first or fourth contact elements Measuring the additional fifth current, (f) measuring an additional fifth voltage across the second and third contact elements, (g) based on the additional fifth current and the additional fifth voltage calculating an additional fifth resistance (R _a), or (g ') the step of holding the fifth resistance (R _a) from the step of determining the distance to an additional fifth resistance (R _a), And (h) an additional sixth potential across said second and third contact elements. Applying to generate an additional sixth current in the surface portion at the first position, (i) measuring the additional sixth current passing through the second or third contact element, (j) the second Measuring an additional sixth voltage across the first and fourth contact elements, and (k) calculating an additional sixth resistance value R _{A '} based on the additional sixth current and the additional sixth voltage, Or (k ') retaining the sixth resistance value R _A' from determining the distance as an additional fifth resistance value R _{A '} , and (l) the additional fifth resistance value R _A ) and a fifth resistance average of the additional sixth resistance value R _{A ′} (

) And (d ") applying an additional first potential across said first and third contact elements to generate an additional first current in said surface portion at said first location, (e") Measuring the additional first current through the first or third contact element, (f ″) measuring an additional first voltage across the second and fourth contact elements, (g ″) the Calculating an additional first resistance value R _B based on an additional first current and the additional first voltage, or (g "') determining the distance as an additional first resistance value R _B. Holding the first resistance value R _B , and (h ″) applying an additional second potential across the second and fourth contact elements to provide an additional second current to the surface portion at the first location. Generating, (i ") a phase passing through said second or said fourth contact element Measuring an additional second current, (j ") measuring an additional second voltage across said first and third contact elements, (k") based on said additional second current and said additional second voltage Calculating the second resistance value R _{B '} , or (k''') determining the distance as the additional second resistance value R _{B '} from the second resistance value R _B' . And (l ″) a sixth resistance average of the additional first resistance value R _B and the additional second resistance value R _{B ′} .

), And (m) the fifth resistance average (

), The sixth resistance average (

), And defining a sixth relation including the eighteenth, nineteenth, and twentieth parameters representing the pseudo sheet resistance R _P , respectively, (n) the fifth resistance average in the sixth relation (

) And the sixth resistance average (

) May be used to determine the pseudo sheet resistance R _P using the eighteenth parameter and the nineteenth parameter, respectively.

과 같을 수 있고, 여기서 R_P는 상기 의사 시트 저항이고,

는 상기 제1 저항 평균이고,

는 상기 제2 저항 평균이다.The sixth relation is

May be equal to, wherein R _P is the pseudo sheet resistance,

Is the first resistance average,

Is the second resistance average.

The hole sheet carrier density N _HS can be calculated as N _HS = B / (ZeR _H ), where B is the magnetic field component perpendicular to the electrically conductive surface portion, Ze is the carrier charge (Z = ± 1), R _H is a hole sheet resistance. The average hole carrier mobility μ _H can be calculated as μ _H = (ZR _H / (R _O B), where Z is dependent on the type of carrier charge ± 1, R _H is a hole sheet resistance, R _O is a sheet resistance, and B is a magnetic field component perpendicular to the electrically conductive surface portion. If the magnetic field is generated by an electromagnet, the magnetic field component B can be theoretically calculated from the current passing through the electromagnet. If the magnetic field is generated by a permanent magnet, the magnetic field component B may be Can be predetermined.

The object of the invention is achieved by an apparatus for determining a distance between a first position on an electrically conductive surface portion of a test sample according to a fourth aspect of the invention and an electrical boundary of the electrically conductive surface portion. A multi-point probe comprising a first contact element, a second contact element, a third contact element, and a fourth contact element, each contact element defining a contact point for establishing electrical contact with the test sample, or The multi-point probe includes a plurality of contact elements-and a control unit configured to perform the method of determining the distance according to the first or second aspect of the present invention.

The object of the invention is achieved by an apparatus for determining electrical properties at a first position on an electrically conductive surface of a test sample according to a fifth aspect of the invention, the apparatus comprising: a first contact element, a second contact element A multi-point probe comprising a third contact element and a fourth contact element, each contact element defining a contact point for establishing electrical contact with the test sample, or The multi-point probe comprises a plurality of contact elements-and a control unit configured to perform a method for determining electrical characteristics at a first location on an electrically conductive surface portion of the test sample according to the third aspect of the invention. Include.

Many embodiments of various aspects of the invention are described below.
1 illustrates a four point probe in contact with an electrically conductive surface portion of a test sample.
2A illustrates the equidistant spacing between the contact points of the contact elements of the probe in a preferred embodiment.
2B illustrates the asymmetric spacing between the contact points of the contact elements of the probe in an alternative embodiment.
2C illustrates the asymmetric spacing between the contact points of the contact elements of the probe in another alternative embodiment.
(1)-(2) of FIG. 3A illustrate a current source and voltage measurement configuration of a contact element according to an alternative embodiment.
(1)-(2) of FIG. 3B and (1)-(2) of FIG. 3C illustrate a current source and voltage measurement configuration of a contact element according to a preferred embodiment.
4A-C illustrate relations for determining distance to electrical boundaries, hole sheet resistance, and sheet resistance in accordance with a preferred embodiment. To illustrate.
5A-5C illustrate relations for determining distance to electrical boundary, hole sheet resistance, and sheet resistance according to an alternative embodiment. To illustrate.
6 illustrates a seven point probe according to an alternative embodiment in contact with an electrically conductive surface portion of a test sample.
7A illustrates the location of the contact point in contact with the test sample.
7B illustrates the location of the contact point that alternatively contacts the test sample.
8 (a)-(4) illustrate the current source and voltage measurement configuration of the contact element of the probe described in connection with FIG.
(1)-(4) of FIG. 8B illustrate an additional current source and voltage measurement configuration of the contact element of the probe described in connection with FIG. 6.
9 is a relational formula for determining a distance to an electrical boundary according to an alternative embodiment described in connection with the probe of FIG. To illustrate.
FIG. 10 illustrates a further relationship for determining the distance to an electrical boundary according to an alternative embodiment described in connection with the probe of FIG. 6.

1 illustrates a multi-point probe 36 in contact with a test sample 30. The test sample 30 is an edge between the side 32 of the test sample 30 and the surface portion 32 corresponding to the electrically conducting surface portion 32 and the upper surface of the test sample 30. It has a boundary 34 that is physically defined by an edge. The side surface 33 is not electrically conductive, so the boundary prevents current from flowing out of the electrically conductive surface portion 32. It is an electrical boundary that prevents.

Multi-point probe 36 has a probe body 18 and at the probe body The first contact element 10, the second contact element 12, the third contact element 14, and the fourth contact element 16 Is extended. Each contact element 10-16 is a cantilever, one end of which is connected to the probe body and the other end defining a contact point 20-26. The contact points 20-26 of the structure of FIG. 1 contact the electrically conductive surface portion 32. Contact elements 10-16 are electrically conductive. Thus, current can pass through each contact element to the electrically conductive surface portion 32. A constant magnetic field B is applied to the test sample 30 to have a field component 38 perpendicular to the electrically conductive surface portion 32.

The contact points 20-26 of the contact elements 10-16 all lie on the common line 40 as shown in FIGS. 2A-C. The electrical boundary 34 has a linear portion 42 and the contact elements 10-16 are oriented such that the common line 40 is parallel to the linear portion 42. The distance or spacing between the contact points 20-22 of the first and second contact elements is denoted by a, the distance or spacing between the contact points 22-24 of the second and third contact elements is denoted by b, The distance or spacing between the contact points 24-26 of the third and fourth contact elements is indicated by c. The distance or spacing between common line 40 and linear portion 42 is indicated by y. In the preferred embodiment shown in FIG. 2A, the distance a-c between the contact points 20-26 of the contact elements is approximately 21 μm. In the alternative embodiment shown in FIG. 2B, the distance a between the contact points 20 ′-22 ′ of the first and second contact elements is approximately 21 μm and the contact points 22 ′ of the second and third contact elements. The distance b between -24 ') is approximately 21 mu m, and the distance c between the contact points 24'-26' of the third and fourth contact elements is approximately 35 mu m. In another alternative embodiment shown in FIG. 2C, the distance a between the contact points 20 ″-22 ″ of the first and second contact elements is approximately 14 μm, and the contact points of the second and third contact elements ( The distance b between 22 " -24 ") is approximately 14 [mu] m and the distance c between the contact points 24 " -26 " of the third and fourth contact elements is approximately 35 [mu] m.

The test sample described in connection with the preferred embodiment of FIG. 2A and the test sample described in connection with the alternative embodiment of FIG. 2B are identical. In these embodiments, the electrical boundary 34 is defined as described in connection with FIG. 1. In an alternative embodiment described in connection with FIG. 2C, the electrical boundary 34 ′ is an electrically conductive surface portion 32 ′ and an electrically non-conducting surface portion on the top surface of the test sample. It is defined as a transition between 44, which means that the two surface portions 34 ', 44 are essentially parallel.

Several electrical properties of the electrically conductive surface portion can be determined. In a preferred embodiment, Hall sheet resistance and sheet resistance are measured using a four point probe having a contact point as shown in FIG. 2A. Is measured.

Positioning of the contact points 20-26 The first position on the electrically conductive surface portion 32 at a distance y from the electrical boundary 34. define. As shown in (1) of FIG. 3B, the current I is injected into the surface portion through the first contact element 10 and at least a part of the current is drained through the third contact element 14. An electric potential is applied across the first and third contact elements 10 and 14. Passing through the first contact element 10 The voltage V _A across the current I and the second and fourth contact elements 12 and 16 is measured and the first resistance value R _B is calculated by dividing the voltage V _A by the current I. Next, as shown in (2) of FIG. 3B, the current I is injected into the surface portion through the second contact element 12 and at least a part of the current is drained through the fourth contact element 14. An electric potential is applied across the second and fourth contact elements 12 and 14. The current I passing through the second contact element 12 and the voltage V _{A '} across the first and third contact elements 10 and 14 are measured and the voltage By dividing V _{A '} by the current I, the second resistance value R _{B ′} is calculated. Next, the first resistance difference ΔR _{BB ′} defined by the difference between the first resistance value R _B and the second resistance value R _{B ′} is calculated as follows.

(1.1)

(1.1)

)도 다음과 같이 계산된다.In addition, the average between the third resistance value R _B and the fourth resistance value R _{B ′} (

) Is also calculated as:

(1.2)

(1.2)

As shown in (1) of FIG. 3C, the currents I and I are injected into the surface portion through the first contact element 10 and at least a portion of the current is drained through the second contact element 12. A potential is applied across the second contact element. The current I passing through the first contact element 10 and the voltage V _C across the third and fourth contact elements 14 and 16 are measured and the third resistance value R _{C is} obtained by dividing the voltage V _C by the current I. ) Is calculated. Next, as shown in (2) of FIG. 3B, the current I is injected into the surface portion through the third contact element 14 and at least a part of the current is drained through the fourth contact element 16. An electric potential is applied across the third and fourth contact elements 14 and 16. First by dividing the third contact element 14, the current I and the first and the second contacting elements 10 and 12 the voltage V _C across _"it is measured, the voltage V _{C 'passing} through the current I a fourth resistance ( R _{C '} ) is calculated. Next, the second resistance difference ΔR _{CC ′} defined by the difference between the third resistance value R _C and the fourth resistance value R _{C ′} is calculated as follows.

(1.3)

(1.3)

)도 다음과 같이 계산된다.In addition, the average between the third resistance value R _C and the fourth resistance value R _{C ′} (

) Is also calculated as:

(1.4)

(1.4)

Many relationships corresponding to a mathematical model of a four point probe in contact with a test sample as shown in FIG. 2A are defined as follows.

(1.5)

(1.5)

(1.6)

(1.6)

Where s represents the spacing between neighboring probe arms, which is the same for all pairs of neighboring probe arms, ie s = a = b = c, ΔR _{BB ′} represents the first resistance difference, y Represents the distance between the contact points 20-26 and the electrical boundary 34, ΔR _{CC '} represents the second resistance difference, and R _H is an electrically conductive surface on which contact is established by the four point probe 36 The hole sheet resistance at the first position of the part 32 is shown. In FIG. 4C, relation f ₁ (Equation 1.5) is shown in dashed lines and relation f ₂ (Equation 1.6) is shown in dashed lines.

The ratio between the two relations (Equations 1.4 and 1.3) described above is used to define the following first relation.

(1.7)

(1.7)

It can also be expressed as

(1.8)

(1.8)

That is, the first relation is a function of the distance y normalized to the nominal interval s. These relationships (Equations 1.7 and 1.8) are shown in solid lines in the graph of FIG. 4C. Next, the measured first and second resistance differences ΔR _{BB ′} and ΔR _{CC ′} are used to derive the normalized distance y / s in the first relation (Equation 1.8). For example, ΔR _{CC '} / ΔR _BB' If the ratio is 0.2, the normalized distance y / s will be approximately 2, and if the ΔR _{CC '} / ΔR _BB ratio is 0.4, the normalized distance y / s will be approximately 5.5, which can be seen from FIG. 4C. Since the nominal spacing s is known, the distance y is easily determined from the normalized distance y / s. If the normalized distance y / s is 2, the value of the function f ₁ will be approximately 0.5. If the normalized distance y / s is 5.5, the value of the function f ₁ will be approximately 0.08. Next, the relationship between the measured first resistance difference ΔR _{BB ′} and Equation 1.3 is described. In combination Hall sheet resistance R _H . Also, f ₂ may also be used in a similar manner.

이 다음과 같이 수학식 1.2 및 1.4로 정의된 저항 평균

및

의 합으로 계산된다.The first resistance average is used to determine sheet resistance, ie, other electrical properties other than hole sheet resistance, of the electrically conductive surface portion.

The resistance average defined by equations 1.2 and 1.4

And

Is calculated as the sum of.

(1.9)

(1.9)

Next, The pseudo sheet resistance R _P is determined from the van der Pauw equation.

(1.10)

(1.10)

A second relationship for determining the sheet resistance of the electrically conductive surface portion contacted by the four point probe is defined as follows. In other words,

이고, (1.11)

And (1.11)

Where R _P is the pseudo sheet resistance, R ₀ is the sheet resistance, and g is a function of the normalized distance y / s. The function g is geometric in that it does not depend on the actual size or dimensions of the four point probe. A function g representing a four point probe using an equidistant contact probe as in FIG. 2A is shown in FIG. 4B. For example, if the normalized distance y / s is 2, the value of the function g, ie R _P / R _0, will be approximately 1.40, and if the normalized distance y / s is 5.5, the corresponding value, or ratio, will be approximately 1.14. Will be. Next, using the pseudo sheet resistance R _P determined as described in relation to Equations 1.9 and 1.10, the sheet resistance R ₀ is easily calculated from Equation 1.11.

In a second embodiment, the hole sheet resistance and sheet resistance are measured using an asymmetric four point probe as shown in FIG. 2B.

Positioning of the contact points 20'-26 ' The first position on the electrically conductive surface portion 32 at a distance y from the electrical boundary 34. define. As shown in (1) of FIG. 3B, the currents I and I are injected into the surface portion through the first contact element 10 and at least a portion of the current is drained through the third contact element 14. An electric potential is applied across the third contact element 10 and 14. The current I passing through the first contact element 10 and the voltage V _B across the second and fourth contact elements 12 and 16 are measured and the first resistance value R _B by dividing the voltage V _B by the current. This is calculated. Next, as shown in (2) of FIG. 3B, the current I is injected into the surface portion through the second contact element 12 and at least a part of the current is drained through the fourth contact element 14. An electric potential is applied across the second and fourth contact elements 12 and 14. The second contact element 12, the current I and the first and passing through the third contact element (10 and 14), the second resistor as a _", and the measurement, the voltage V _B, the voltage V _B across the dividing by the current value I ( R _{B '} ) is calculated. Next, the first resistance difference ΔR _{BB ′} defined by the difference between the first resistance value R _B and the second resistance value R _{B ′} is calculated as follows.

(2.1)

(2.1)

)도 다음과 같이 계산된다.In addition, the average between the third resistance value R _B and the fourth resistance value R _{B ′} (

) Is also calculated as:

(2.2)

(2.2)

As shown in (1) of FIG. 3C, the currents I and I are injected into the surface portion through the first contact element 10 and at least a portion of the current is drained through the second contact element 12. A potential is applied across the second contact element. The current I passing through the first contact element 10 and the voltage V _C across the third and fourth contact elements 14 and 16 are measured and the third resistance value R _{C is} obtained by dividing the voltage V _C by the current I. ) Is calculated. Next, as shown in (2) Fig. 3b, a current I is injected to the surface portion through the third contact element 14, at least a part of the current to a drain through the fourth contact element 16 An electric potential is applied across the third and fourth contact elements 14 and 16. First by dividing the third contact element 14, the current I and the first and the second contacting elements 10 and 12 the voltage V _C across _"it is measured, the voltage V _{C 'passing} through the current I a fourth resistance ( R _{C '} ) is calculated. Next, the second resistance difference ΔR _{CC ′} defined by the difference between the third resistance value R _C and the fourth resistance value R _{C ′} is calculated as follows.

(2.3)

(2.3)

)도 다음과 같이 계산된다.In addition, the average between the third resistance value R _C and the fourth resistance value R _{C ′} (

) Is also calculated as:

(2.4)

(2.4)

As shown in (1) of FIG. 3A, current I is injected into the surface portion through the first contact element 10 and at least a portion of the current is drained through the fourth contact element 16. An electric potential is applied across the first and fourth contact elements 10 and 16. The current I passing through the first contact element 10 and the voltage V _A across the second and third contact elements 12 and 14 are measured and the fifth resistance value R _A by dividing the voltage V _A by the current I ) Is calculated. Next, as shown in (2) of FIG. 3A, the current I is injected into the surface portion through the second contact element 12 and at least a part of the current is drained through the third contact element 14. A potential is applied across the second and third contact elements 12 and 14. The current I passing through the second contact element 12 and the voltage V _{A '} across the first and fourth contact elements 10' and 16 are measured and the sixth resistance value is obtained by dividing the voltage V _{A '} by the current I. (R _{A '} ) is calculated. Next, the third resistance difference ΔR _{AA ′} defined by the difference between the fifth resistance value R _A and the sixth resistance value R _{B ′} is calculated as follows.

(2.5)

(2.5)

)도 다음과 같이 계산된다.In addition, the average between the fifth resistance value R _A and the sixth resistance value R _{A ′} (

) Is also calculated as:

(2.6)

(2.6)

Many relations corresponding to the mathematical model of a four point probe in contact with a test sample as shown in FIG. 2C are defined as follows.

(2.7)

(2.7)

(2.8)

(2.8)

(2.9)

(2.9)

Where a, b, and c represent the spacing between the contact points as shown in FIG. 2C, y represents the distance between the contact points 20'-26 'and the electrical boundary 34, and ΔR _BB' is the first resistor ΔR _{CC ′} represents the second resistance difference, ΔR _{AA ′} represents the third resistance difference, and R _H represents an electrically conductive surface portion where contact is established by the four-point probe 36. The hole sheet resistance at that position of 32 is shown. In FIG. 5C, relation f ₁ (Equation 2.7) is shown as dashed-dotted line, relation f ₂ (Equation 2.8) is shown as dashed line and relation f ₃ (Equation 2.9) is shown as dashed line.

Next, the first relational expression As follows Is defined.

(2.10)

(2.10)

It can also be expressed as

(2.11)

Wherein α is 1, that is, the first relation is a function of the distance y and the spacings a, b, and c between the contact points. These relations (Equations 2.10 and 2.11) are shown in solid lines in the graph of FIG. 5C. Next, the measured first, second, and third resistance differences ΔR _{BB ′ ,} ΔR _CC , and ΔR _{AA ′} are normalized distances 3y / (a +) in the first relation (Equation 2.11). b + c). For example, (ΔR _{AA ′} + ΔR _{CC ′} ) / ΔR _{BB ′} If the ratio is 0.2, then the normalized distance 3y / (a + b + c) will be approximately 0.5, ΔR _{CC '} / ΔR _BB If the ratio is 0.8 the normalized distance 3y / (a + b + c) will be approximately 7, which can be seen from FIG. 5C. Since the nominal spacings a, b, and c are known, the distance y is easily determined from the normalized distance 3y / (a + b + c). For example, when the interval of FIG. 2C, i.e., a = b = 14 μm and c is 35 μm, if the normalized distance 3y / (a + b + c) is 0.5, the distance y will be approximately 10.5 μm, If the normalized distance 3y / (a + b + c) is 7, the distance y will be approximately 147 μm. Also, if the normalized distance 3y / (a + b + c) is 0.5, the value of the function f ₂ will be approximately 1.33. If the normalized distance 3y / (a + b + c) is 7, the value of the function f ₂ will be It will be approximately 0.04. Next, the relationship between the measured first resistance difference ΔR _{BB ′} and Equation 2.8 is given. When used in combination, hole sheet resistance _RH is obtained. In addition, the function f ₁ And f ₃ can also be used in a similar manner.

In order to determine the sheet resistance of the electrically conductive surface portion, the pseudo sheet resistance R _P is first determined from the following Vander Pow equation.

(2.12)

(2.12)

Next, another second relation for determining sheet resistance of the electrically conductive surface portion contacted by the four point probe is as follows. Is defined. In other words,

(2.13)

(2.13)

Where R _P is the pseudo sheet resistance, R ₀ is the sheet resistance, and g is a function of the normalized distance y and the spacing a, b, and c between the contact points. Asymmetrically spaced contact probes as in FIG. A function g representing the four point probe used is shown in FIG. 5B. For example, if the distance y is approximately 10.5 μm, the value of the function g, or ratio R _P / R ₀ , will be approximately 1.44. Next, using the pseudo sheet resistance R _P determined as described in connection with Equation 2.12, the sheet resistance R ₀ is easily calculated from Equation 2.13.

More general examples of determining hole sheet resistance and sheet resistance using symmetrical probes are presented herein. For a symmetrical four point probe whose contact points are equidistant, i.e., a = b = c = s, the data processing of FIG. 3B, FIG. 3B, FIG. 2B, FIG. 3C, and FIG. (2) the resistance value _{R B, R B ', R} C, and R _C' is configured only four measurements B, B is needed ', C and C' respectively as shown in Fig. The following is derived from the resistance values.

(3.1)

(3.1)

(3.2)

(3.2)

Using the mean, same The pseudo sheet resistance R _P is calculated from the bander power equation.

(3.3)

(3.3)

(3.4)

(3.4)

Resistance difference △ R _{BB '} And ΔR _{CC '} is It is represented by the same known function.

(3.5)

(3.5)

(3.6)

(3.6)

Therefore, ΔR _{BB '} And the ratio of _{ΔR CC ′} may be expressed as a function of y as follows.

(3.7)

(3.7)

In this equation, the function f can be obtained from theoretical calculations or numerical simulations as plotted in FIG. 4A. Using this plot, the distance y is determined, and then the hole sheet resistance R _H can be solved from Equation 3.5 or Equation 3.6.

In addition, pseudo sheet resistance R _P And the ratio of sheet resistance R ₀ can be expressed by a known function g which depends only on y / s as follows.

(3.8)

(3.8)

The function g can be obtained from theoretical calculations or numerical simulations and is plotted in FIG. 4B. Finally, using this plot and pseudo sheet resistance R _P from Equation 3.4, sheet resistance R ₀ is calculated.

A more general example of determining hole sheet resistance and sheet resistance using an asymmetric probe is presented here. For asymmetric four point probes with a, b, and c spacing between the contact points of the contact elements, the data processing of FIG. 3A, FIG. 3A, FIG. 3A, FIG. 3B, FIG. 3B, and FIG. As shown in (2), (1) of FIG. 3C, and (2) of FIG. 3C, the resistance values are R _A , R _{A '} , R _B , R _B' , R _C , and R _{C '} , respectively. Six configurations A, A ', B, B', C and C 'are all required. Only five of these configurations are independent. The intervals a = 14um, b = 14um, and c = 35um as shown in FIG. 2C are used in the following example, in which case It is derived from the resistance values.

(4.1)

(4.1)

(4.2)

(4.2)

(4.3)

(4.3)

Using the mean, The pseudo sheet resistance R _P is calculated from the bander power equation.

(4.4)

(4.4)

Resistance difference △ R _{AA '} , △ R _BB' And ΔR _{CC '} are represented by the following known functions.

(4.5)

(4.5)

(4.6)

(4.6)

(4.7)

(4.7)

Thus, the following ΔR _{AA '} , ΔR _BB' which depend only on distance y And ΔR _{CC '} can be defined.

(4.8)

(4.8)

In this equation, the function f can be obtained from theoretical calculations or numerical simulations. By tuning the factor α, the function f is optimized so that distance detection is less sensitive to probe position error. It has been found that for a = 14 μm, b = 14 μm, and c = 35 μm, α = 1 is a good choice and the function f can be plotted as shown in FIG. 5A. Using this plot, the distance y is determined, and then the hole sheet resistance R _H can be solved from Equation 4.5, Equation 4.6, or Equation 4.7.

In addition, pseudo sheet resistance R _P And the ratio of sheet resistance R ₀ is It can be represented by the same known function g.

(4.9)

(4.9)

The function g can be obtained from theoretical calculations or numerical simulations and is plotted in FIG. 5B. Finally, using this plot and pseudo sheet resistance R _P from Equation 4.4, sheet resistance R ₀ is calculated.

6 illustrates a multi point probe 36 ′ in contact with the test sample 30 ′. The test sample 30 'is provided between the electrically conductive surface portion 32' and between the surface portion 32 corresponding to the upper surface of the test sample 30 'and the side surface 33' of the test sample 30 '. It has a boundary 34 'physically defined by the edge. Side 33 'is not electrically conductive, so the boundary prevents current from flowing out of the electrically conductive surface portion 32'. It is an electrical boundary.

The multi point probe 36 ′ has a probe body 18 ′ with seven contact elements 50-62 extending from the probe body. Each contact element 50-62 is a flexible cantilever, one end of which is connected to the probe body 18 ′ and the other end defining a contact point 70-82. The contact points 70-82 of the structure of FIG. 6 contact the electrically conductive surface portion 32 ′. Contact elements 50-62 are electrically conductive. Thus, current can pass through each contact element 50-62 to an electrically conductive surface portion 32 ′. A constant magnetic field B is applied to the test sample 30 ′ to have a magnetic field component 38 ′ perpendicular to the electrically conductive surface portion 32.

A contact element of a first configuration is defined which consists of first, second, third and fourth contact elements corresponding to the contact elements 50, 54, 58 and 62, respectively. A contact element of a second configuration is defined, which consists of fifth, sixth, seventh and eighth contact elements corresponding to the contact elements 56, 58, 60, and 62, respectively. Here, the first and second configurations both comprise contact elements 58 and 62.

The contact points 70-82 of the contact elements 50-62 all lie on a common line 90 when in contact as shown in FIG. 7A. The electrical boundary 34 'has a linear portion 42' and the contact elements 50-62 are oriented so that the common line 40 'is parallel to the linear portion 42'. The nominal distance or spacing between the contacts 70-82 is approximately equal and denoted by s. The distance or spacing between common line 90 and linear portion 42 ' denoted by y. In the alternative embodiment shown in FIG. 7A, the distance s between the contact points 70-82 of the contact elements is approximately 10 μm. Thus, the contact points of the contact element of the first configuration define an effective separation or spacing s ₁ of 2s, ie s ₁ is approximately 20 μm, while the contact points of the contact element of the second configuration are effective separation or spacing of 1 s. s ₂ is defined, ie s ₂ is approximately 10 μm.

In the alternative contact shown in FIG. 7B, the surface portion 32 ′ is not flat, which means that the three contact elements 70-74 are different from the other four contact elements 76-82. To combine with Respectively. Thus, the contact element of the first configuration defines an average distance y ₁ to the line portion 42 ′ which is different from the corresponding additional average distance y ₂ of the second configuration.

In the contact of FIG. 7A, contact points 70-82 define a distance y to electrical boundary 34. As shown in (1) of FIG. 8A, currents I are injected into the surface portion through the first contact element 50 and at least a portion of the current is drained through the third contact element 58. An electric potential is applied across the third contact element 50 and 58. The current I passing through the first contact element 50 and the voltage V _{B , 1} across the second and fourth contact elements 54 and 62 are measured and the first resistor is divided by dividing the voltage V _{B , 1} by the current I. The value R _{B , 1} is calculated. Next, as shown in (2) of FIG. 8A, the current I is injected into the surface portion through the second element 54, and at least a portion of the current is drained through the fourth contact element 62. A potential is applied across the second and fourth contact elements 54 and 62. The current I through the second contact element 54 and the voltage V _{B ' , 1} across the first and third contact elements 50 and 58 are measured, and the voltage V _{B' , 1} divided by the current I 2 The resistance value R _{B ' , 1} is calculated. Next, the first resistance difference ΔR _{BB ′, 1} defined as the difference between the first resistance value R _{B , 1} and the second resistance value R _{B ′ , 1} is calculated as follows.

(5.1)

(5.1)

)도 다음과 같이 계산된다.In addition _, the first resistance average between the third resistance value R _{B , 1} and the fourth resistance value R _{B ′ , 1} (

) Is also calculated as:

(5.2)

(5.2)

As shown in (3) of FIG. 8A, currents I are injected into the surface portion through the fifth contact element 56 and at least a portion of the current is drained through the seventh contact element 60. A potential is applied across the seventh contact element 56 and 60. The current I through the fifth contact element 56 and the voltage V _{B , 2} across the sixth and eighth contact elements 58 and 62 are measured and the third resistor is divided by dividing the voltage V _{B, 2} by the current I. The value R _{B , 2} is calculated. Next, as shown in (4) of FIG. 8A, the current I is injected into the surface portion through the sixth contact element 58 and at least a part of the current is drained through the eighth contact element 62. Sixth and eighth contact elements 58 And 62) potentials are applied at both ends. The current I through the sixth contact element 58 and the voltage V _{B ' , 2} across the fifth and seventh contact elements 56 and 60 are measured and the voltage V _{B' , 2} divided by the current I 4 The resistance value R _{B ' , 2} is calculated. Next, the second resistance difference _{ΔR BB′2} defined as the difference between the third resistance value R _{B , 2} and the fourth resistance value R _{B ′ , 2} is calculated as follows.

(5.4)

(5.4)

)도 다음과 같이 계산된다. In addition _, the second resistance average between the third resistance value R _{B , 2} and the fourth resistance value R _{B ′ , 2} (

) Is also calculated as:

(5.5)

(5.5)

The function corresponding to the mathematical model of a four point probe It is defined as follows.

(5.6)

(5.6)

Where s represents the effective spacing between neighboring probe arms, ΔR _{BB ′} represents the first resistance difference, y represents the distance between the contact point 70-82 and the electrical boundary 34 ', and ΔR _{CC ′} represents 2 represents the resistance difference, and R _H represents the hole sheet resistance at the first position of the electrically conductive surface portion 32 ′ where contact is established by the four point probe 36 ′. In Fig. 9, the function f (s, y) is shown as a function of y when the interval s ₁ is 20 mu m (long wave) and the interval s ₂ is 10 mu m (short wave). The first relation is defined as the ratio between two functions formed from (Equation 5.6) by two different intervals as follows.

(5.7)

(5.7)

This relation is shown by the function f _D (s ₁ , s ₂ , y) (solid line) of the distance y in the graph of FIG. 9. Next, the measured first and second resistance differences ΔR _{BB ′, 1} and ΔR _{BB ′, 2} are used to derive the distance y in the first relation (Equation 5.4). For example, if the ΔR _{CC '} / ΔR _BB' ratio is 1, the distance y will be approximately 19. Next, the relationship between the measured first resistance difference ΔR _{BB ′ , 1} and the nominal interval s ₁ = 20 μm and Equation 5.6 is given. When used in combination, hole sheet resistance _RH is obtained. In addition, the nominal spacing s ₂ = 10 μm may also be used in a similar manner.

)이 다음과 같이 계산된다.In order to improve the accuracy of the determination of the distance y, By doing To a further model of contact of FIG. 7A I use it. As shown in (1) of FIG. 8B, the currents I and I are injected into the surface portion through the first contact element 50 and at least a portion of the current is drained through the fourth contact element 62. A potential is applied across the fourth contact element 50 and 62. The current I through the first contact element 50 and the voltage V _{B, 1} across the second and third contact elements 54 and 58 are measured and the fifth resistor is divided by dividing the voltage V _{A , 1} by the current I. The value R _{A , 1} is calculated. Next, as shown in (2) of FIG. 8B, the current I is The second and third contact elements 54 are injected into the surface portion through the second contact element 54, such that at least a portion of the current is drained through the third contact element 58. And 58) a potential is applied at both ends. The current I passing through the second contact element 54 and the voltage V _{B ' , 1} across the first and fourth contact elements 50 and 62 are measured, and by dividing the voltage V _{A' , 1} by the current I 6 The resistance value (R _{A ' .1} ) is calculated. Next, a third resistance average between the fifth resistance value R _{A , 1} and the sixth resistance value R _{A ′ , 1} (

) Is calculated as follows.

(5.8)

(5.8)

)이 다음과 같이 계산된다.As shown in (3) of FIG. 8B, the fifth and fifth portions are arranged such that the current I is injected into the surface portion through the fifth contact element 56, and at least a part of the current is drained through the eighth contact element 62. An electric potential is applied across the eighth contact elements 56 and 62. The current I through the fifth contact element 56 and the voltage V _{B , 2} across the sixth and seventh contact elements 58 and 60 are measured and the seventh resistor is divided by dividing the voltage V _{A , 2} by the current I. The value R _{A , 2} is calculated. Next, as shown in (4) of FIG. 8B, the current I is injected into the surface portion through the sixth contact element 58 and at least a part of the current is drained through the seventh contact element 60. A potential is applied across the sixth and seventh contact elements 58 and 60. The current I through the sixth contact element 58 and the voltage VB _{' , 2} across the fifth and eighth contact elements 56 and 62 are measured and the voltage The eighth resistance value R _{A ′ , 2} is calculated by dividing V _{B ′, 2} by the current I. Next, a fourth resistance average between the fifth resistance value R _{A, 1} and the sixth resistance value R _{A ' , 1} (

) Is calculated as follows.

(5.9)

(5.9)

The bander powder equation is Is defined.

(5.10)

(5.10)

) 및 (

)(수학식 5.2 및 5.8)는 밴더 파우어 수학식(수학식 5.10)에서 제1 의사 시트 저항(R_{P ,1})을 도출하는데 사용된다. 마찬가지로, 제2 및 제4 저항차(

) 및 (

)(수학식 5.5 및 5.9)는 밴더 파우어 수학식(수학식 5.10)에서 제2 의사 시트 저항(R_{P ,2})을 도출하는데 사용된다.Where R _P is the pseudo sheet resistance and the first and third resistance differences (

) And (

(Equations 5.2 and 5.8) are used to derive the first pseudo sheet resistance R _{P , 1} in the bander power equation (Equation 5.10). Similarly, the second and fourth resistance difference (

) And (

(Equations 5.5 and 5.9) are used to derive the second pseudo sheet resistance R _{P , 2} in the bander power equation (Equation 5.10).

The function corresponding to the mathematical model of the four point probe described with reference to FIG. 6 is defined as follows.

(5.11)

(5.11)

Where R _P is the pseudo sheet resistance, considered as a function of the spacing s between neighboring probe arms and the distance y between the contact points 70-82 and the electrical boundary 34 ', and R _s represents the sheet resistance of the contact point. First interval s ₁ = 20 μm and second interval s ₂ = 10 μm The function g (s, y) of the case is derived, which is shown in FIG. 10 (long wave and short wave, respectively). These two functions are then used to form a fourth relation as follows.

(5.12)

(5.12)

This is also shown in FIG. 10 (solid line). Next, the first and second pseudo sheet resistors R _P , 1 and R _{P , 2} are used to derive the value of the distance y in the fourth relation, which can be made graphically in FIG. 10. The function g _D (s ₁ , s ₂ , y), which can be derived analytically or numerically, is not a monotone function and defines a peak value at a specific distance. Therefore, it will not uniquely determine the distance y. The fourth relation (Equation 5.12) will typically determine the distance y more accurately than the first relation (Equation 5.7). Thus, the first relation is used to derive an auxiliary distance, which is used to determine the distance y of the peak value from the fourth relation, ie uniquely determine the distance y.

In an alternative embodiment, the first relation (Equation 5.7) and the fourth relation (Equation 5.12) are the distances between the linear elements 42 'and the contact elements of the first configuration, as described in connection with FIG. 7B. It is modified to take into account the difference of the additional distance y ₂ between the linear elements 42 'and the contact elements of y ₁ and the second configuration. The first relation (Equation 5.7) is redefined as follows:

(5.13)

(5.13)

And the fourth relation (Equation 5.11) is redefined as follows.

(5.14)

(5.14)

Two functions f _D (s ₁ , s ₂ , y ₁ , y ₂ ) and g _D (s ₁ , s ₂ , y ₁ , y ₂ ) can be derived analytically or numerically. Next, the derived first and second resistance differences (Equations 5.1 and Equation 5.4) and the first, second, third and fourth resistance averages (Equation 5.2, Equation 5.5, Equation 5.8 and Equation 5). 5.9) is defined in the first and fourth relations (Equations 5.13 and 5.14) overridden with known nominal spacings s ₁ = 20 μm and s ₂ = 10 μm, for example by regression analysis. It is used to derive the distance y ₁ and the additional distance y ₂ simultaneously.

The features of the present invention are as follows.

1. The distance between a first location on an electrically conductive surface portion of a test sample and an electrical boundary of the electrically conductive surface portion includes a first contact element, a second contact element, a third contact element, and a fourth contact element. A method as determined by a multi-point probe, wherein each contact element defines a contact point for establishing electrical contact with the test sample.

(i) contacting the test sample with the first contact element, the second contact element, the third contact element, and the fourth contact element at the first location on the electrically conductive surface portion,

(ii) applying a magnetic field having a main magnetic field component perpendicular to the electrically conductive surface portion at the first position,

(iii) applying a first potential across the first and third contact elements to generate a first current in the surface portion at the first position,

(iv) measuring the first current through the first or third contact element,

(v) measuring a first voltage across the second and fourth contact elements,

(vi) calculating a first resistance value R _B based on the first current and the first voltage,

(vii) applying a second potential across the second and fourth contact elements to generate a second current in the surface portion at the first position,

(viii) measuring the second current through the second or fourth contact element,

(ix) measuring a second voltage across the first and third contact elements,

(x) calculating a second resistance value R _{B ′} based on the second current and the second voltage,

(xi) calculating a first resistance difference ΔR _{BB ′} based on the difference between the first resistance value and the second resistance value,

(xii) applying a third potential across the first and second contact elements to generate a third current in the surface portion at the first location,

(xiii) measuring the third current through the first or second contact element,

(xiv) measuring a third voltage across the third and fourth contact elements,

(xv) calculating a third resistance value R _C based on the third current and the third voltage,

(xvi) applying a fourth potential across the third and fourth contact elements to generate a fourth current in the surface portion at the first location,

(xvii) measuring the fourth current through the third or fourth contact element,

(xviii) measuring a fourth voltage across the first and second contact elements,

(xix) calculating a fourth resistance value R _{C ′} based on the fourth current and the fourth voltage,

(xx) calculating a second resistance difference ΔR _{CC ′} based on the difference between the third resistance value and the fourth resistance value,

(xxi) a first relation f including first, second, and third parameters representing the first resistance difference, the second resistance difference, and the distance between the first position and the electrical boundary, respectively; Defining,

(xxii) using the first and second resistance differences ΔR _{BB ′} and ΔR _{CC ′ as} the first and second parameters, respectively, in the first relation, between the first position and the electrical boundary. Determining the distance y.

2. The method of feature 1, wherein the contact point defines a first line that intersects each of the contact points.

3. The second aspect of the invention, wherein the electrical boundary has an approximately linear portion and is on the first position and the linear portion. And the distance between one point is shorter than the distance between the first position and any point on the electrical boundary outside the linear portion.

4. The third feature is to:

(xxxiv) orienting the multi-point probe to be positioned in the first line in a parallel relationship with the linear portion.

5. First to fourth features The method of any one of the preceding claims, wherein the spacing between the first and second contact elements, the second and third contact elements, and the contact points of the third and fourth contact elements are approximately equal.

6. The feature of any one of features 1-5 wherein the first relation is equal to _{ΔR CC ′} / ΔR _{BB ′} = f (y, s), where ΔR _{BB ′} is the first resistor. Difference, and ΔR _{CC '} is The second resistance difference, and f is a function comprising as a parameter the distance y between the first position and the electrical boundary and the spacing s between the contact points.

와 같고, 여기서 △R_BB'는 상기 추가적인 제1 저항차(△R_BB')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내고, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내며, 상기 관계식 △R_CC'/△R_BB'=f(y,s)에서 상기 제2 저항차 △R_CC'는

와 같고, 여기서 △R_CC'는 상기 추가적인 제2 저항차(△R_CC')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내는 것을 특징으로 하는 방법.
7. In the sixth aspect, the first resistance difference ΔR _{BB ′} is expressed in the relation ΔR _{CC ′} / ΔR _{BB ′} = f (y, s).

ΔR _{BB ′} denotes the additional first resistance difference ΔR _{BB ′} , y denotes the distance y, and a denotes the distance between the contact points of the first and second contact elements. B denotes an interval between the contact points of the second and third contact elements, c denotes an interval between the contact points of the third and fourth contact elements, and the relation ΔR _{CC ′} / ΔR _{BB ′} = At f (y, s), the second resistance difference ΔR _{CC ′} is

ΔR _{CC ′} represents the additional second resistance difference ΔR _{CC ′} , y represents the distance y, and a represents the distance between the contact points of the first and second contact elements. And b represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements.

8. The device according to any one of the first to fourth features,

(xxiii) applying a fifth potential across the first and fourth contact elements to generate a fifth current in the surface portion at the first location,

(xxiv) measuring the fifth current through the first or fourth contact element,

(xxv) measuring a fifth voltage across the second and third contact elements,

(xxvi) calculating a fifth resistance value R _A based on the fifth current and the fifth voltage,

(xxvii) applying a sixth potential across the second and third contact elements to generate a sixth current in the surface portion at the first location,

(xxviii) measuring the sixth current through the second or third contact element,

(xxix) measuring a sixth voltage across the first and fourth contact elements,

(xxx) calculating a sixth resistance value R _{A ′} based on the sixth current and the sixth voltage,

(xxxi) calculating a third resistance difference ΔR _{AA ′} based on the difference between the fifth resistance value and the sixth resistance value,

(xxxii) when defining the first relation (f), further including a fourth parameter representing the third resistance difference ΔR _{AA ′ in} the first relation f, and

(xxxiii) when determining the distance y between the first position and the electrical boundary, the first and second resistance differences ΔR used as the first and second parameters in the first relation, respectively. _{And using} the third resistance difference ΔR _{AA ′} as the fourth parameter in addition to _{BB ′} and ΔR _{CC ′} . ≪ / RTI >

9. The feature of feature 8, wherein the contact points are arranged in line, wherein the spacing between the contact points of the first and second contact elements and the spacing between the contact points of the second and third contact elements are approximately equal. How to.

10. The touch point of any of the eighth and ninth features, wherein the contact points are arranged in a line and the spacing between the contact points of the third and fourth contact elements is the contact point of the first and second contact elements. The interval between them and different.

11. The feature of clause 10, wherein the spacing between the contact points of the third and fourth contact elements is in the range 1.1-3.7, 1.2-3.3, 1.3-2.9 than the spacing between the contact points of the first and second contact elements. At least one of, 1.4-2.5, 1.5-2.1, and 1.6-1.7, and / or the range 1.2-1.3, 1.3-1.4, 1.4-1.5, 1.5-1.6, 1.6-1.7, 1.7-1.8, 1.8-1.9, 1.9 A factor within one of -2.0, 2.0-2.2, 2.2-2.4, 2.4-2.6, 2.6-2.8, 2.8-3.0, 3.0-3.3, 3.3-3.6, 3.6-3.9, and / or approximately 5 divided by 3, Or one or more of the ranges 1.2-3.8, 1.6-3.4, 1.8-3.2, 2.0-3.0, 2.2-2.8, and 2.4-2.6, and / or ranges 1.2-1.3, 1.3-1.4, 1.4-1.5, 1.5-1.6, Within one of 1.6-1.7, 1.7-1.8, 1.8-1.9, 1.9-2.0, 2.0-2.2, 2.2-2.4, 2.4-2.6, 2.6-2.8, 2.8-3.0, 3.0-3.3, 3.3-3.6, 3.6-3.9 A factor, and / or as large as approximately five divided by two.

12. The method according to any one of features 8 to 11, wherein the spacing between the contact points of the first and second contact elements is in the range 1-5 μm, 5-10 μm, 10-15 μm, 15-20 Μm, 20-25 μm, 25-30 μm, 30-40 μm, 40-50 μm, 50-500 μm, and / or range 1-50 μm, 5-40 μm, 10-30 μm, 15- And at least one of 25 μm.

13. The feature of any one of features 8-12, wherein the first relation is (ΔR _{AA ′} + αΔR _{CC ′} ) / ΔR _{BB ′} = f (y, a, b, c) and ΔR _{BB ′} is the first resistance difference, ΔR _{CC ′} is the second resistance difference, ΔR _{AA ′} is the third resistance difference, and α is a tuning factor in the range of −10 to 10. factor), f is a function including the distance y between the first position and the electrical boundary, a is the distance between the contact points of the first and second contact elements, and b is the second and second 3 said spacing between said contact points of a contact element, and c is said spacing between said contact points of said third and fourth contact elements.

14. The method of feature 13, wherein the tuning factor α is about 1 or about −1.

와 같고, 여기서 △R_BB'는 상기 추가적인 제1 저항차(△R_AA')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내고, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내며, 상기 관계식(△R_AA'+α△R_CC')/△R_BB'= f(y,a,b,c)에서 상기 제2 저항차 △R_CC'는

와 같고, 여기서 △R_CC'는 상기 추가적인 제2 저항차(△R_CC')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내고, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내며, 상기 관계식(△R_AA'+α△R_CC')/△R_BB'= f(y,a,b,c)에서 상기 제3 저항차 △R_AA'는

와 같고, 여기서 △R_{A A'}는 상기 추가적인 제3 저항차(△R_AA')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 상기 간격을 나타내는 것을 특징으로 하는 방법.
15. The method according to any one of features 13 and 14, wherein the relation (ΔR _{AA ′} + αΔR _{CC ′} ) / ΔR _{BB ′} = f (y, a, b, c) in the first aspect. Resistance difference △ R _{BB '} is

ΔR _{BB ′} represents the additional first resistance difference ΔR _{AA ′} , y represents the distance y, and a represents the distance between the contact points of the first and second contact elements. B denotes the spacing between the contact points of the second and third contact elements, c denotes the spacing between the contact points of the third and fourth contact elements, and the relationship (ΔR _{AA ′} + αΔR _{CC) '} ) / ΔR _BB' = f (y, a, b, c), the second resistance difference ΔR _{CC '} is

ΔR _{CC ′} represents the additional second resistance difference ΔR _{CC ′} , y represents the distance y, and a represents the distance between the contact points of the first and second contact elements. B denotes the spacing between the contact points of the second and third contact elements, c denotes the spacing between the contact points of the third and fourth contact elements, and the relationship (ΔR _{AA ′} + αΔR _{CC) '} ) / ΔR _BB' = f (y, a, b, c), the third resistance difference ΔR _{AA '} is

ΔR _{A A ′} represents the additional third resistance difference ΔR _{AA ′} , y represents the distance y, and a is the spacing between the contact points of the first and second contact elements. And b represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements.

16. The method of any of features 1-15, wherein the spacing between the contact points of the first and second contact elements is in the range 0.1-100 μm, 1-90 μm, 10-80 μm, 20-. At least one of 70 μm, 30-60 μm, and 40-50 μm, and / or range 0.1-1 μm, 1-10 μm, 10-20 μm, 20-30 μm, 30-40 μm, 40-50 μm , 50-60 μm, 60-70 μm, 70-80 μm, 80-90 μm, 90-100 μm, or 100-500 μm.

17. A method of determining electrical properties at a first location on an electrically conductive surface portion of a test sample, wherein the electrically conductive surface portion has an electrical boundary, the method comprising:

(a) the feature according to any one of features 1 to 16; Determining a distance y between the first location on the electrically conductive surface portion of the test sample and the electrical boundary of the electrically conductive surface portion,

(b) defining a second relational expression comprising a fifth parameter indicative of said electrical characteristic and said distance y, and

(c) determining said electrical property using said distance y as said fifth parameter in said second relationship.

18. The feature of feature 17, wherein the second relation further comprises the spacing between the contact points of the first contact element, the second contact element, the third contact element, and / or the fourth contact element,

(b ') When defining the second relation, the second relation defines the distance between the contact points of the first contact element, the second contact element, the third contact element, and / or the fourth contact element. Further comprising a ninth parameter, wherein

and (c ') the interval is used as the ninth parameter in addition to the first distance y in the second relation in determining the electrical property.

19. The feature of any one of features 17 and 18, wherein the electrical property is a hole sheet resistance (R _H ) and the second relation (f ₁ , f ₂ ) is an additional first resistance difference ΔR _{BB ′.} And a sixth parameter in which the method comprises

(d) applying an additional first potential across the first and third contact elements to generate an additional first current in the surface portion at the first location,

(e) measuring the additional first current through the first or third contact element,

(f) measuring an additional first voltage across the second and fourth contact elements,

(g) calculating an additional first resistance value R _B based on the additional first current and the additional first voltage, or

(g ') the step of retaining said first resistance value (R _B) from the step of determining the distance to the additional first resistance value (R _B), and

(h) applying an additional second potential across the second and fourth contact elements to generate an additional second current at the surface portion at the first location,

(i) measuring the additional second current through the second or fourth contact element,

(j) measuring an additional second voltage across the first and third contact elements,

(k) calculating an additional second resistance value R _{B '} based on the additional second current and the additional second voltage, or

(k ') the step of retaining said second resistance value (R _B') from the step of determining the distance further second resistance value (R _{B 'to),} and

(l) calculating the additional first resistance difference ΔR _{BB ′} based on the difference between the additional first resistance value and the additional second resistance value, or

(l ') retaining the first resistance difference (R _{BB ′} ) from determining the distance as the additional first resistance difference (ΔR _{BB ′} ).

와 같고, 여기서 △R_{B B'}는 상기 추가적인 제1 저항차(△R_BB')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내는 것을 특징으로 하는 방법.
20. The feature of feature 19, wherein the second relation is

ΔR _{B B ′} represents the additional first resistance difference ΔR _{BB ′} , y represents the distance y, and a is the spacing between the contact points of the first and second contact elements. And b represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements.

21. The device of any one of features 17 and 18, wherein the electrical property is a hole sheet resistance (R _H ) and the second relation (f ₂ , f ₃ ) is an additional second resistance difference ΔR _{CC ′.} And a sixth parameter in which the method comprises

(d) applying an additional third potential across the first and second contact elements to generate an additional third current at the surface portion at the first location,

(e) measuring the additional third current through the first or second contact element,

(f) measuring an additional third voltage across the third and fourth contact elements,

(g) calculating an additional third resistance value R _C based on the additional third current and the additional third voltage, or

(g ') the step of retaining said second resistance value (R _C) from the step of determining the distance to the additional first resistance value (R _C), and

(h) applying an additional fourth potential across the third and fourth contact elements to generate an additional fourth current in the surface portion at the first location,

(i) measuring the additional fourth current through the third or fourth contact element,

(j) measuring an additional fourth voltage across the first and second contact elements,

(k) calculating an additional fourth resistance value R _{C ′} based on the additional fourth current and the additional fourth voltage, or

(k ') adding the distance to the first _'From the step of determining a second resistance value (R _C the resistance value (R _C), comprising: holding a), and

(l) calculating the additional second resistance difference ΔR _{CC ′} based on the difference between the additional third resistance value and the additional fourth resistance value, or

(l '), characterized in that it comprises the step of holding said second resistance difference (△ R _CC') from the step of determining in the second additional resistance difference (△ R _CC the distance _") more.

와 같고, 여기서 △R_CC'는 상기 추가적인 제2 저항차(△R_CC')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내는 것을 특징으로 하는 방법.
22. The method of feature 21, wherein the second relation is

ΔR _{CC ′} represents the additional second resistance difference ΔR _{CC ′} , y represents the distance y, and a represents the distance between the contact points of the first and second contact elements. And b represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements.

23. The feature of any one of features 17 and 18, wherein the electrical property is a hole sheet resistance R _H and the second relation f ₁ represents an additional third resistance difference ΔR _{AA ′} . And a sixth parameter, wherein the method further comprises:

(d) applying an additional fifth potential across the first and fourth contact elements to generate an additional fifth current at the surface portion at the first location,

(e) measuring the additional fifth current through the first or fourth contact element,

(f) measuring an additional fifth voltage across the second and third contact elements,

(g) calculating an additional fifth resistance value R _A based on the additional fifth current and the additional fifth voltage, or

(g ') a step of holding the fifth resistance (R _A) from the step of determining the distance to an additional fifth resistance (R _A), and

(h) applying an additional sixth potential across the second and third contact elements to generate an additional sixth current in the surface portion at the first location,

(i) measuring the additional sixth current through the second or third contact element,

(j) measuring an additional sixth voltage across the first and fourth contact elements,

(k) calculating an additional sixth resistance value R _{A '} based on the additional sixth current and the additional sixth voltage, or

(k ') adding the distance to the fifth _'From the step of determining the value of the sixth resistance (R _A resistance value (R _A), comprising: holding a), and

(l) calculating the additional third resistance difference ΔR _{AA ′} based on the difference between the additional fifth resistance value and the additional sixth resistance value, or

(l '), characterized in that it comprises the step of holding the third resistance difference (△ R _AA') from the step of determining by said additional third resistance difference (△ R _AA the distance _") more.

와 같고, 여기서 △R_AA'는 상기 추가적인 제3 저항차(△R_AA')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내는 것을 특징으로 하는 방법.
24. The feature of clause 23, wherein the second relation is

ΔR _{AA ′} represents the additional third resistance difference ΔR _{AA ′} , y represents the distance y, and a represents the distance between the contact points of the first and second contact elements. And b represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements.

25. The method of any one of features 17-18, wherein the electrical property is sheet resistance R ₀ and the second relation g further comprises a sixth parameter indicative of the pseudo sheet resistance R _P. The method is

(d) applying an additional fifth potential across the first and fourth contact elements to generate an additional fifth current at the surface portion at the first location,

(e) measuring the additional fifth current through the first or fourth contact element,

(f) measuring an additional fifth voltage across the second and third contact elements,

(g) calculating an additional fifth resistance value R _A based on the additional fifth current and the additional fifth voltage, or

(g ') a step of holding the fifth resistance (R _A) from the step of determining the distance to an additional fifth resistance (R _A), and

(h) applying an additional sixth potential across the second and third contact elements to generate an additional sixth current in the surface portion at the first location,

(i) measuring the additional sixth current through the second or third contact element,

(j) measuring an additional sixth voltage across the first and fourth contact elements,

(k) calculating an additional sixth resistance value R _{A '} based on the additional sixth current and the additional sixth voltage, or

(k ') holding the sixth resistance value R _A' from determining the distance as an additional fifth resistance value R _{A '} , and

)을 계산하는 단계, 및(l) a first resistance average of the additional fifth resistance value R _{A ′} and the additional sixth resistance value R _{A ′} (

), And

(d ") Applying an additional first potential across the first and third contact elements to generate an additional first current in the surface portion at the first location,

(e ") measuring said additional first current through said first or third contact element,

(f ") measuring an additional first voltage across said second and fourth contact elements,

(g ") calculating an additional first resistance value R _B based on said additional first current and said additional first voltage, or

(g ''') comprising: holding the first resistance value (R _B) from the step of determining the distance to the additional first resistance value (R _B), and

(h ") applying an additional second potential across said second and fourth contact elements to generate an additional second current in said surface portion at said first location,

(i ") measuring said additional second current through said second or fourth contact element,

(j ") measuring an additional second voltage across said first and third contact elements,

(k ″) calculating an additional second resistance value R _{B ′} based on the additional second current and the additional second voltage, or

(k ''') holding the second resistance value R _B' from determining the distance as an additional second resistance value R ' _B , and

)을 계산하는 단계, 및(l ″) a second resistance average of the additional first resistance value R _B and the additional second resistance value R _{B ′} (

), And

), 상기 제2 저항 평균(

), 및 상기 의사 시트 저항(R_P)을 각각 나타내는 제7, 제8, 및 제9 파라미터를 포함하는 제3 관계식을 정의하는 단계,(m) the first resistance average (

), The second resistance average (

), And defining a third relational expression including seventh, eighth, and ninth parameters representing the pseudo sheet resistance R _P , respectively;

) 및 상기 제2 저항 평균(

)을 각각 상기 제7 파라미터 및 상기 제8 파라미터로서 이용하여 상기 의사 시트 저항(R_P)을 결정하는 단계를 더 포함하는 것을 특징으로 하는 방법.
(n) the first resistance average in the third relation

) And the second resistance average (

) Determining the pseudo sheet resistance R _P using the seventh and eighth parameters, respectively.

와 같고, 여기서 R_P는 상기 의사 시트 저항이고,

는 상기 제1 저항 평균이며,

는 상기 제2 저항 평균인 것을 특징으로 하는 방법.
26. The feature of feature 25, wherein the third relational expression is

, Wherein R _P is the pseudo sheet resistance,

Is the first resistance average,

Is the second resistance average.

27. An apparatus for determining a distance between a first location on an electrically conductive surface portion of a test sample and an electrical boundary of the electrically conductive surface portion;

A multi-point probe comprising a first contact element, a second contact element, a third contact element, and a fourth contact element, each contact element defining a contact point for establishing electrical contact with the test sample; and

According to any of the features 1 to 16 And a control unit configured to perform the method of determining the distance.

28. An apparatus for determining electrical properties at a first location on an electrically conductive surface of a test sample, wherein

A multi-point probe comprising a first contact element, a second contact element, a third contact element, and a fourth contact element, each contact element defining a contact point for establishing electrical contact with the test sample; and

And a control unit configured to perform a method of determining electrical characteristics at a first location on an electrically conductive surface portion of the test sample according to any one of features 17 to 26.

Further features of the present invention are as follows.

1. The distance between a first location on an electrically conductive surface portion of a test sample and an electrical boundary of the electrically conductive surface portion includes a first contact element, a second contact element, a third contact element, and a fourth contact element. A method as determined by a multi-point probe, wherein each contact element defines a contact point for establishing electrical contact with the test sample.

(i.i) contacting the test sample with the first contact element, the second contact element, the third contact element, and the fourth contact element at the first location on the electrically conductive surface portion,

(i.ii) applying a magnetic field having a main magnetic field component perpendicular to the electrically conductive surface portion at the first position,

(i.iii) applying a first potential across the first and third contact elements to generate a first current in the surface portion at the first location,

(i.iv) measuring the first current through the first or third contact element,

(i.v) measuring a first voltage across the second and fourth contact elements,

(i.vi) calculating a first resistance value R _B based on the first current and the first voltage,

(i.vii) applying a second potential across the second and fourth contact elements to generate a second current in the surface portion at the first position,

(i.viii) measuring the second current through the second or fourth contact element,

(i.ix) measuring a second voltage across the first and third contact elements,

(ix) calculating a second resistance value R _{B ′} based on the second current and the second voltage,

(i.xi) calculating a first resistance difference ΔR _{BB ′} based on a difference between the first resistance value and the second resistance value,

(i.xii) applying a third potential across the first and second contact elements to generate a third current in the surface portion at the first location,

(i.xiii) measuring the third current through the first or second contact element,

(i.xiv) measuring a third voltage across the third and fourth contact elements,

(i.xv) calculating a third resistance value R _C based on the third current and the third voltage,

(i.xvi) applying a fourth potential across the third and fourth contact elements to generate a fourth current in the surface portion at the first position,

(i.xvii) measuring the fourth current through the third or fourth contact element,

(i.xviii) measuring a fourth voltage across the first and second contact elements,

(i.xix) calculating a fourth resistance value R _{C ′} based on the fourth current and the fourth voltage, and

(i.xx) calculating a second resistance difference ΔR _{CC ′} based on the difference between the third resistance value and the fourth resistance value,

Or in the alternative, the multi-point probe includes a plurality of contact elements, each contact element defining a contact point for establishing electrical contact with the test sample, the plurality of contact elements defining the first contact element, The second contact element, the third contact element, the fourth contact element and one or more additional contact elements, wherein steps (i.xii) to (i.xx) are carried out in the following steps, i.e.

(ii.xii) defining a contact element of a first configuration of the plurality of contact elements, wherein the contact element of the first configuration comprises the first contact element, the second contact element, the third contact element, and the Consisting of the fourth contact element-,

(ii.xiii) defining a contact element of a second configuration of the plurality of contact elements, wherein the contact element of the second configuration is a fifth contact element, a sixth contact element, a seventh contact element, and an eighth contact element. Wherein at least one of the contact elements of the second configuration is a contact element of the one or more additional contact elements,

(ii.xiv) contacting the test sample with the contact element of the contact element of the second configuration at the first location on the electrically conductive surface portion and simultaneously bringing the test sample into the contact element of the contact element of the first configuration. Contacting with the contact element,

(ii.xv) applying a third potential across the fifth and seventh contact elements to generate a third current in the surface portion at the first position,

(ii.xvi) measuring the third current through the fifth or seventh contact element,

(ii.xvii) measuring a third voltage across the sixth and eighth contact elements,

(ii.xviii) calculating a third resistance value R _{B , 2} based on the third current and the third voltage,

(ii.xix) applying a fourth potential across the sixth and eighth contact elements to generate a fourth current in the surface portion at the first position,

(ii.xx) measuring the fourth current through the sixth or eighth contact element,

(ii.xxi) measuring a fourth voltage across the fifth and seventh contact elements,

(ii.xxii) calculating a fourth resistance value R _{B ′ , 2} based on the fourth current and the fourth voltage, and

(ii.xxiii) calculating a second resistance difference ΔR _{BB ′ , 2} based on the difference between the third resistance value and the fourth resistance value,

Alternatives comprising the steps (i.xii) to (i.xx) and alternatives comprising the steps (ii.xii) to (ii.xxii) all,

(i.xxi) A first relation f comprising first, second, and third parameters representing the first resistance difference, the second resistance difference, and the distance between the first position and the electrical boundary, respectively. ), And

(i.xxii) wherein the using in the first equation of the first and second resistance difference _{(△ R BB ', △ R} CC', △ R BB ', 2) to each of the first and a second parameters Determining the third parameter indicative of the distance y between one location and the electrical boundary.

2. The first further feature and an alternative to replacing steps (i.xii) to (i.xx) above,

)을 계산하는 단계,(iii.xxiv) a first average resistance of the first resistance value (R _B) and said second resistance value (R _{B ')} (

),

)을 계산하는 단계,(iii.xxv) a second resistance average of the third resistance value R _{B , 2} and the fourth resistance value R _{B ′ , 2} ;

),

(iii.xxvi) applying a fifth potential across the first and fourth contact elements to generate a fifth current in the surface portion at the first location,

(iii.xxvii) measuring the fifth current through the first or fourth contact element,

(iii.xxviii) measuring a fifth voltage across the second and third contact elements,

(iii.xxix) calculating a fifth resistance value R _{A , 1} based on the fifth current and the fifth voltage,

(iii.xxx) applying a sixth potential across the second and third contact elements to generate a sixth current in the surface portion at the first location,

(iii.xxxi) measuring the sixth current through the second or third contact element,

(iii.xxxii) measuring a sixth voltage across the first and fourth contact elements,

(iii.xxxiii) calculating a sixth resistance value R _{A ′ , 1} based on the sixth current and the sixth voltage,

)을 계산하는 단계, (iii.xxxiv) a third resistance average of the fifth resistance value R _{A , 1} and the sixth resistance value R _{A ′ , 1} ;

),

(iii.xxxv) applying a seventh potential across the fifth and eighth contact elements to generate a seventh current in the surface portion at the first position,

(iii.xxxvi) measuring the seventh current through the fifth or eighth contact element,

(iii.xxxvii) measuring a seventh voltage across the sixth and seventh contact elements,

(iii.xxxviii) calculating a seventh resistance value R _{A , 2} based on the seventh current and the seventh voltage,

(iii.xxxix) applying an eighth potential across the sixth and seventh contact elements to generate an eighth current in the surface portion at the first position,

(iii.xl) measuring the eighth current through the sixth or seventh contact element,

(iii.xli) measuring an eighth voltage across the fifth and eighth contact elements,

(iii.xlii) calculating an eighth resistance value R _{A ′ , 2} based on the eighth current and the eighth voltage,

)을 계산하는 단계,(iii.xliii) a fourth resistance average of the seventh resistance value R _{A , 2} and the eighth resistance value R _{A ′ , 2} (

)of Calculating,

), 상기 제3 저항 평균(

), 및 제1 의사 시트 저항(R_{P ,1})을 각각 나타내는 제4, 제5, 및 제6 파라미터를 포함하는 제2 관계식을 정의하는 단계,(iii.xliv) the first resistance average (

), The third resistance average (

), And defining a second relationship comprising fourth, fifth, and sixth parameters representing the first pseudo sheet resistance R _{P , 1} , respectively,

) 및 상기 제3 저항 평균(

)을 각각 상기 제4 파라미터 및 상기 제5 파라미터로서 이용하여 상기 제1 의사 시트 저항(R_{P ,1})을 나타내는 상기 제6 파라미터를 결정하는 단계,(iii.xlv) the average of the first resistance in the second relation (

) And the third resistance average (

Determining each of the sixth parameters representing the first pseudo sheet resistance R _{P , 1 using} R as the fourth parameter and the fifth parameter, respectively.

), 상기 제4 저항 평균(

), 및 제2 의사 시트 저항(R_{P ,2})을 각각 나타내는 제7, 제8, 및 제9 파라미터를 포함하는 제3 관계식을 정의하는 단계,(iii.xlvi) the second resistance average (

), The fourth resistance average (

), And defining a third relationship comprising seventh, eighth, and ninth parameters representing the second pseudo sheet resistance R _{P , 2} , respectively,

) 및 상기 제4 저항 평균(

)을 각각 상기 제7 파라미터 및 상기 제8 파라미터로서 이용하여 상기 제2 의사 시트 저항(R_{P ,2})을 나타내는 상기 제9 파라미터를 결정하는 단계,(iii.xlvii) the second resistance mean in the third relation

) And the fourth resistance average (

Determining the ninth parameter representing the second pseudo sheet resistance R _{P , 2} using each of the seventh parameter and the eighth parameter,

(iii.xlviii) the tenth and the third representing the first pseudo sheet resistance R _{P , 1} , the second pseudo sheet resistance R _{P , 2} , and the distance between the first position and the electrical boundary, respectively. Defining a fourth relation g _D comprising 11, and a twelfth parameter, and

(iv.xlix) the first and second pseudo sheet resistances R _{P , 1} , R _{P, 2 in} the fourth relation g _{D as} the tenth and eleventh parameters, respectively; Determining the twelfth parameter indicative of an additional distance y between a location and the electrical boundary,

Alternatively, in the alternative, the contact element of the second configuration may add an additional distance y ₂ between the first location on the electrically conductive surface portion of the test sample and the electrical boundary of the electrically conductive surface portion. Wherein the first relation (f _D ) further comprises a thirteenth parameter indicative of the additional distance between the first position and the electrical boundary, and the fourth relation (g _D ) comprises the first position and the electrical boundary Further comprising a fourteenth parameter indicative of said additional distance between Step (iii.xlix) is the next step, i.e.

(iv.xlix) the first and second pseudo sheet resistances R _{P , 1} , R _{P, 2 in} the fourth relation g _{D as} the tenth and eleventh parameters, respectively; And simultaneously determining the thirteenth parameter and the fourteenth parameter indicative of the distance y and the additional distance y ₂ between the position and the electrical boundary.

3. Second additional feature and remind Containing steps (iii.xlix) In an alternative embodiment, the fourth relationship is equal to R _{P , 1} / R _{P , 2} = g _D (y), where R _{P , 1} represents the first pseudo sheet resistance, and R _{P , 2} represents the first 2 represents a pseudo sheet resistance, g _D represents a function comprising the distance y as a parameter, the function g _D defines a peak value at a specific distance, and the function g _D is such that the function of the distance is less than the specified distance Increase when and decrease when the function of the distance is above the specific distance,

(iii.xlx) comparing the distance with the specific distance to determine whether the additional distance is less than or greater than the specific distance in the fourth relational expression.

4. A method for determining, by a multi-addition point probe comprising a plurality of contact elements, a distance between a first position on an electrically conductive surface portion of a test sample and an electrical boundary of the electrically conductive surface portion, wherein each contact element is Define a contact point for establishing electrical contact with the test sample, the plurality of contact elements including a first contact element, a second contact element, a third contact element, a fourth contact element and one or more additional contact elements; , The method,

(vi) defining a contact element of a first configuration of the plurality of contact elements, wherein the contact element of the first configuration comprises the first contact element, the second contact element, the third contact element, and the fourth contact element; Consisting of contact elements-,

(v.ii) defining a contact element of a second configuration of the plurality of contact elements, wherein the contact element of the second configuration comprises a fifth contact element, a sixth contact element, a seventh contact element, and an eighth contact element; Wherein at least one of the contact elements of the second configuration is a contact element of the one or more additional contact elements,

(v.iii-iv) contacting the test sample with the contact element of the contact element of the first and second configurations at the first location on the electrically conductive surface portion,

(v.v) applying a magnetic field having a main magnetic field component perpendicular to the electrically conductive surface portion at the first position,

(v.vi) applying a first potential across the first and third contact elements to generate a first current in the surface portion at the first location,

(v.vii) measuring the first current through the first or third contact element,

(v.viii) measuring a first voltage across the second and fourth contact elements,

(v.ix) calculating a first resistance value R _B based on the first current and the first voltage,

(v.x) applying a second potential across the second and fourth contact elements to generate a second current in the surface portion at the first position,

(v.xi) measuring the second current through the second or fourth contact element,

(v.xii) measuring a second voltage across the first and third contact elements,

(v.xiii) calculating a second resistance value R _{B ′} based on the second current and the second voltage,

)을 계산하는 단계,(v.xiv) a first average resistance of the first resistance value (R _B) and said second resistance value (R _{B ')} (

),

(v.xv) applying a third potential across the fifth and seventh contact elements to generate a third current at the surface portion at the first position,

(v.xvi) measuring the third current through the fifth or seventh contact element,

(v.xvii) measuring a third voltage across the sixth and eighth contact elements,

(v.xviii) calculating a third resistance value R _{B , 2} based on the third current and the third voltage,

(v.xix) applying a fourth potential across the sixth and eighth contact elements to generate a fourth current in the surface portion at the first position,

(v.xx) measuring the fourth current through the sixth or eighth contact element,

(v.xxi) measuring a fourth voltage across the fifth and seventh contact elements,

(v.xxii) calculating a fourth resistance value R _{B ′ , 2} based on the fourth current and the fourth voltage,

)을 계산하는 단계,(v.xxv) A second resistance average of the third resistance value R _{B , 2} and the fourth resistance value R _{B ′ , 2} (

),

(v.xxvi) applying a fifth potential across the first and fourth contact elements to generate a fifth current in the surface portion at the first location,

(v.xxvii) measuring the fifth current through the first or fourth contact element,

(v.xxviii) measuring a fifth voltage across the second and third contact elements,

(v.xxix) calculating a fifth resistance value R _{A , 1} based on the fifth current and the fifth voltage,

(v.xxx) applying a sixth potential across the second and third contact elements to generate a sixth current in the surface portion at the first location,

(v.xxxi) measuring the sixth current through the second or third contact element,

(v.xxxii) measuring a sixth voltage across the first and fourth contact elements,

(v.xxxiii) calculating a sixth resistance value R _{A ′ , 1} based on the sixth current and the sixth voltage,

)을 계산하는 단계, (v.xxxiv) a third resistance average of the fifth resistance value R _{A , 1} and the sixth resistance value R _{A ′ , 1}

),

(v.xxxv) applying a seventh potential across the fifth and eighth contact elements to generate a seventh current in the surface portion at the first position,

(v.xxxvi) measuring the seventh current through the fifth or eighth contact element,

(v.xxxvii) measuring a seventh voltage across the sixth and seventh contact elements,

(v.xxxviii) calculating a seventh resistance value R _{A , 2} based on the seventh current and the seventh voltage,

(v.xxxix) applying an eighth potential across the sixth and seventh contact elements to generate an eighth current in the surface portion at the first position,

(v.xl) measuring the eighth current through the sixth or seventh contact element,

(v.xli) measuring an eighth voltage across the fifth and eighth contact elements,

(v.xlii) calculating an eighth resistance value R _{A ′ , 2} based on the eighth current and the eighth voltage,

)을 계산하는 단계,(v.xliii) a fourth resistance average of the seventh resistance value R _{A , 1} and the eighth resistance value R _{A ′ , 2} (

),

), 상기 제3 저항 평균(

), 및 제1 의사 시트 저항(R_{P ,1})을 각각 나타내는 제4, 제5, 및 제6 파라미터를 포함하는 제2 관계식을 정의하는 단계,(v.xliv) the first resistance average (

), The third resistance average (

), And defining a second relationship comprising fourth, fifth, and sixth parameters representing the first pseudo sheet resistance R _{P , 1} , respectively,

) 및 상기 제3 저항 평균(

)을 각각 상기 제4 파라미터 및 상기 제5 파라미터로서 이용하여 상기 제1 의사 시트 저항(R_{P ,1})을 나타내는 상기 제6 파라미터를 결정하는 단계,(v.xlv) the first resistance average in the second relation

) And the third resistance average (

Determining each of the sixth parameters representing the first pseudo sheet resistance R _{P , 1 using} R as the fourth parameter and the fifth parameter, respectively.

), 상기 제4 저항 평균(

), 및 제2 의사 시트 저항(R_{P ,2})을 각각 나타내는 제7, 제8, 및 제9 파라미터를 포함하는 제3 관계식을 정의하는 단계,(v.xlvi) the second resistance average (

), The fourth resistance average (

), And defining a third relationship comprising seventh, eighth, and ninth parameters representing the second pseudo sheet resistance R _{P , 2} , respectively,

) 및 상기 제4 저항 평균(

)을 각각 상기 제7 파라미터 및 상기 제8 파라미터로서 이용하여 상기 제2 의사 시트 저항(R_{P ,2})을 나타내는 상기 제9 파라미터를 결정하는 단계,(v.xlvii) the second resistance average in the third relation

) And the fourth resistance average (

Determining the ninth parameter representing the second pseudo sheet resistance R _{P , 2} using each of the seventh parameter and the eighth parameter,

(v.xlviii) the tenth and the fifth representing the first pseudo sheet resistance R _{P , 1} , the second pseudo sheet resistance R _{P , 2} , and the distance between the first position and the electrical boundary, respectively. Defining a fourth relation g _D comprising 11, and a twelfth parameter, and

(v.xlix) the first and second pseudo sheet resistances R _{P , 1} , R _{P, 2 in} the fourth relation g _{D as} the tenth and eleventh parameters, respectively; Determining the twelfth parameter indicative of the value of the distance y between a location and the electrical boundary.

5. The fourth additional feature, wherein the fourth relation is equal to R _{P , 1} / R _{P , 2} = g _D (y), where R _{P , 1} represents the first pseudo sheet resistance, R _{P , 2} represents the second pseudo sheet resistance, g _D represents a function comprising the distance y as a parameter, the function g _D defines a peak value at a specific distance, and the function g _D is a function of the distance Increases when less than the specific distance and decreases when the function of the distance is greater than or equal to the specific distance;

(v.xlx) of the first to third additional features In one feature Determining a distance indicative of an auxiliary distance by said method, and

(v.xlxi) further comprising comparing the auxiliary distance with the specific distance and determining whether the distance is less than or greater than the specific distance in the fourth relational expression.

6. The method according to any of the first to fifth additional features, wherein the contact point defines a first line that intersects each of the contact points.

7. The method according to any one of the first to sixth additional features, wherein The contact points of the first contact element, the second contact element, the third contact element, the fourth contact element, and the one or more additional contact elements before each contact point with the test sample intersect with each of the contact points. Defining a first line.

8. The seventh further feature, wherein the contact points of the first contact element, the second contact element, the third contact element, and the fourth contact element are arranged in a predetermined order along the first line. How to feature.

9. The eighth further feature, wherein the contact points of the fifth contact element, the sixth contact element, the seventh contact element, and the eighth contact element are arranged in a predetermined order along the first line. How to feature.

10. The contact element of any of the eighth and ninth additional features, wherein the first and second contact elements, the second and third contact elements, and the contact elements of the third and fourth contact elements. Wherein the spacing is approximately equal to the first spacing value s ₁ .

11. The contact element of any of the eighth to tenth additional features, wherein the fifth and sixth contact elements, the sixth and seventh contact elements, and the contact elements of the seventh and eighth contact elements. Wherein the spacing is approximately equal to the second spacing value s ₂ .

12. Eleventh Additional Features and remind In an alternative alternative to steps (i.xii) to (i.xx), the first relation is equal to ΔR _{BB ′} / ΔR _{BB ′ , 2} = f _D (y, s ₁ , s ₂ ) Where _{ΔR BB ′} represents the first resistance difference, _{ΔR BB′2} represents the second resistance difference, f _D is the distance y between the first position and the electrical boundary, and the first spacing value s ₁ , and the second interval value s ₂ .

와 같은 것을 특징으로 하는 방법.
13. The method of claim 12 further feature, the first relational expression _{△ R BB '/ △ R BB} ', 2 = f D (y, s 1, s 2) from the function _{f D (y, s 1,} s 2) Is

And characterized in that.

과 같고, 여기서 R_{P , 1}는 상기 제1 의사 시트 저항을 나타내고,

는 상기 제1 저항 평균이고,

은 상기 제3 저항 평균이며, 상기 제3 관계식은

과 같고, 여기서 R_{P ,2}는 상기 제2 의사 시트 저항을 나타내고,

는 상기 제2 저항 평균이며,

는 상기 제4 저항 평균인 것을 특징으로 하는 방법.
14. The feature of any of the second to thirteenth additional features, wherein the second relationship is

Wherein R _{P , 1} represents the first pseudo sheet resistance,

Is the first resistance average,

Is the third resistance average, and the third relational expression is

, Where R _{P , 2} represents the second pseudo sheet resistance,

Is the second resistance average,

Is the fourth resistance average.

15. A feature comprising any of the second to fourteenth additional features and the step (iii.xlix) above. In an alternative embodiment, the fourth relationship is equal to R _{P , 1} / R _{P , 2} = g _D (y, s ₁ , s ₂ ), where R _{P , 1} represents the first pseudo sheet resistance, R _{P , 2} represents the second pseudo sheet resistance, g _D is a function comprising the distance y between the first position and the electrical boundary, the first spacing value s ₁ , and the second spacing value s ₂ Characterized in that the method.

16. Any of the second to fourteenth additional features and the step (iii.xlix) above In an alternative alternative, the first relationship is ΔR _{BB ′} / ΔR _{BB ′, 2} = f _D (y, y ₂ , s ₁ , s ₂ ), where ΔR _{BB ′} is the first resistor. DELTA R _BB'2 represents the second resistance difference, f _D represents the distance y and the additional distance y ₂ between the first position and the electrical boundary, the first spacing value s ₁ , and the And a second interval value s ₂ .

와 같은 것을 특징으로 하는 방법.
17. The twelfth additional feature, the function f _D (y, y ₂ ,) in the first relation ΔR _{BB ′} / ΔR _{BB ′ , 2} = f _D (y, y ₂ , s ₁ , s ₂ ) s ₁ , s ₂ )

And characterized in that.

18. Any one of the second to fourteenth additional features and replacing step (iii.xlix) above In an alternative embodiment, the fourth relationship is equal to R _{P, 1} / R _{P, 2} = g _D (y, y ₂ , s ₁ , s ₂ ), where R _{P , 1} represents the first pseudo sheet resistance , R _{P , 2} represents the second pseudo sheet resistance, g _D is the distance y and the additional distance y ₂ between the first position and the electrical boundary, the first spacing value s ₁ , and the second spacing A function comprising a value s ₂ .

19. The feature of any of the sixth through eighteenth features, wherein the electrical boundary is approximately a linear portion. And the distance between the first location and the additional point on the linear portion is shorter than the distance between the first location and any additional point on the electrical boundary outside the linear portion.

20. The nineteenth additional feature of

(vi.i) orienting the multi additional point probe to be in the first line in a parallel relationship with the linear portion.

21. The method according to any of the first to twentieth features, wherein the first and second contact elements, the second and third contact elements, and the connection points of the third and fourth contact elements are between. Wherein the spacing is about the same.

22. Any of the first to twenty-first additional features and remind Comprising steps (i.xii) to (i.xx) In an alternative embodiment, the first relation is equal to _{ΔR CC ′} / ΔR _{BB ′} = f (y, s), where ΔR _{BB ′} represents the first resistance difference, and ΔR _{CC ′} represents the first relationship. 2 represents a resistance difference, and f is a function comprising as a parameter the distance y between the first position and the electrical boundary and the spacing s between the contact points.

와 같고, 여기서 △R_BB'는 상기 추가적인 제1 저항차(△R_BB')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내고, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내며, 상기 관계식 △R_CC'/△R_{B B'}=f(y,s)에서 상기 제2 저항차 △R_CC'는

와 같고, 여기서 △R_CC'는 상기 추가적인 제2 저항차(△R _CC' )를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내는 것을 특징으로 하는 방법.
23. Article according to a further feature 22, wherein the relational expression _{△ R CC '/ △ R BB} ' = f (y, s) of the first resistance difference △ R _{BB 'from}

ΔR _{BB ′} denotes the additional first resistance difference ΔR _{BB ′} , y denotes the distance y, and a denotes the distance between the contact points of the first and second contact elements. B denotes an interval between the contact points of the second and third contact elements, c denotes an interval between the contact points of the third and fourth contact elements, and the relationship ΔR _{CC ′} / ΔR _{B B ′} At f (y, s), the second resistance difference ΔR _{CC ′} is

ΔR _{CC ′} represents the additional second resistance difference ΔR _{CC ′} , y represents the distance y, and a represents the distance between the contact points of the first and second contact elements. And b represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements.

24. Any one of the first to twenty-third additional features and the above In an alternative comprising the steps (i.xii) to (i.xx),

(i.xxiii) applying a fifth potential across the first and fourth contact elements to generate a fifth current in the surface portion at the first location,

(i.xxiv) measuring the fifth current through the first or fourth contact element,

(i.xxv) measuring a fifth voltage across the second and third contact elements,

(i.xxvi) calculating a fifth resistance value R _A based on the fifth current and the fifth voltage,

(i.xxvii) applying a sixth potential across the second and third contact elements to generate a sixth current in the surface portion at the first location,

(i.xxviii) Measuring the sixth current through the second or third contact element,

(i.xxix) measuring a sixth voltage across the first and fourth contact elements,

(i.xxx) calculating a sixth resistance value R _{A ′} based on the sixth current and the sixth voltage,

(i.xxxi) calculating a third resistance difference ΔR _{AA ′} based on the difference between the fifth resistance value and the sixth resistance value,

(i.xxxii) when defining the first relation f, further including a fourth parameter representing the third resistance difference ΔR _{AA ′ in} the first relation f, and

(i.xxxiii) when determining the distance y between the first position and the electrical boundary, the first and second resistance differences (Δ) used as the first and second parameters in the first relational equation. R _{BB '} , ΔR _CC' ) using the third resistance difference ΔR _{AA '} as the fourth parameter It further comprises a method.

25. The device of any of the first to twenty-fourth additional features , wherein the contact points are disposed in line, the spacing between the contact points of the first and second contact elements, and of the second and third contact elements. And the spacing between the contact points is approximately equal.

26. The method according to any of the first to twenty-fifth additional features, wherein the contact points are arranged in line and the spacing between the contact points of the third and fourth contact elements is greater than that of the first and second contact elements. And a gap between the contact points.

27. The additional aspect 26, wherein the spacing between the contact points of the third and fourth contact elements is in the range 1.1-3.7, 1.2-3.3, 1.3- than the spacing between the contact points of the first and second contact elements. At least one of 2.9, 1.4-2.5, 1.5-2.1, and 1.6-1.7, and / or in the range 1.2-1.3, 1.3-1.4, 1.4-1.5, 1.5-1.6, 1.6-1.7, 1.7-1.8, 1.8-1.9, A factor within one of 1.9-2.0, 2.0-2.2, 2.2-2.4, 2.4-2.6, 2.6-2.8, 2.8-3.0, 3.0-3.3, 3.3-3.6, 3.6-3.9, and / or approximately 5 divided by 3, or one or more of the ranges 1.2-3.8, 1.6-3.4, 1.8-3.2, 2.0-3.0, 2.2-2.8, and 2.4-2.6, and / or 1.2-1.3, 1.3-1.4, 1.4 -1.5, 1.5-1.6, 1.6-1.7, 1.7-1.8, 1.8-1.9, 1.9-2.0, 2.0-2.2, 2.2-2.4, 2.4-2.6, 2.6-2.8, 2.8-3.0, 3.0-3.3, 3.3-3.6 , Factor within one of 3.6-3.9, and / or as large as about five divided by two.

28. The method according to any of the first to 27th additional features, wherein the spacing between the contact points of the first and second contact elements is in the range of 1-5 μm, 5-10 μm, 10-15 μm, 15 -20 μm, 20-25 μm, 25-30 μm, 30-40 μm, 40-50 μm, 50-500 μm, and / or range 1-50 μm, 5-40 μm, 10-30 μm, And at least one of 15-25 μm.

29. The method of any one of items 24 to 28, wherein the first relationship is (ΔR _{AA ′} + αΔR _{CC ′} ) / ΔR _{BB ′} = f (y, a, b, c ΔR _{BB ′} is the first resistance difference, ΔR _{CC ′} is the second resistance difference, ΔR _{AA ′} is the third resistance difference, and α is a tuning factor in the range of −10 to 10. F is a function including the distance y between the first position and the electrical boundary, a is the spacing between the contact points of the first and second contact elements, and b is the second and third contacts The spacing between the contact points of the element, and c is the spacing between the contact points of the third and fourth contact elements.

30. The method of further 29, wherein the tuning factor α is about 1 or about −1.

와 같고, 여기서 △R_BB'는 상기 추가적인 제1 저항차(△R_AA')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내고, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내며, 상기 관계식(△R_AA'+α△R_CC')/△R_BB'= f(y,a,b,c)에서 상기 제2 저항차 △R_CC'는

와 같고, 여기서 △R_CC'는 상기 추가적인 제2 저항차(△R_CC')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내고, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내며, 상기 관계식(△R_AA'+α△R_CC')/△R_BB'= f(y,a,b,c)에서 상기 제3 저항차 △R_AA'는

와 같고, 여기서 △R_AA'는 상기 추가적인 제3 저항차(△R_AA')를 나타내고, y는 상기 거리(y)를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 상기 간격을 나타내는 것을 특징으로 하는 방법.
31. The method according to any one of the 29th additional feature and the 30th additional feature, wherein in the relation (ΔR _{AA ′} + αΔR _{CC ′} ) / ΔR _{BB ′} = f (y, a, b, c) The first resistance difference ΔR _{BB ′} is

ΔR _{BB ′} represents the additional first resistance difference ΔR _{AA ′} , y represents the distance y, and a represents the distance between the contact points of the first and second contact elements. B denotes the spacing between the contact points of the second and third contact elements, c denotes the spacing between the contact points of the third and fourth contact elements, and the relationship (ΔR _{AA ′} + αΔR _{CC) '} ) / ΔR _BB' = the second resistance difference at f (y, a, b, c) ΔR _{CC '} is

ΔR _{CC ′} represents the additional second resistance difference ΔR _{CC ′} , y represents the distance y, and a represents the distance between the contact points of the first and second contact elements. B denotes the spacing between the contact points of the second and third contact elements, c denotes the spacing between the contact points of the third and fourth contact elements, and the relationship (ΔR _{AA ′} + αΔR _{CC) '} ) / ΔR _BB' = f (y, a, b, c), the third resistance difference ΔR _{AA '} is

ΔR _{AA ′} represents the additional third resistance difference ΔR _{AA ′} , y represents the distance y, and a represents the distance between the contact points of the first and second contact elements. And b represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements.

32. The method of any one of the first additional feature and the thirty-first additional feature, wherein the spacing between the contact points of the first and second contact elements ranges from 0.1-100 μm, 1-90 μm, 10-80 μm, At least one of 20-70 μm, 30-60 μm, and 40-50 μm, and / or range 0.1-1 μm, 1-10 μm, 10-20 μm, 20-30 μm, 30-40 μm, 40- And 50-60 μm, 60-70 μm, 70-80 μm, 80-90 μm, 90-100 μm, or 100-500 μm.

33. A method of determining electrical properties at a first location on an electrically conductive surface portion of a test sample, wherein the electrically conductive surface portion has an electrical boundary, the method comprising:

(a) a distance y between said first position on said electrically conductive surface portion of said test sample according to any one of the first to thirty-second additional features and said electrical boundary of said electrically conductive surface portion; Determining the,

(b) defining a fifth relational expression comprising a fifteenth parameter indicative of said electrical characteristic and said distance y, and

(c) determining the electrical property using the additional distance y in the fifth relation as the fifteenth parameter,

Or in the alternative,

(a) an additional distance y between the first position on the electrically conductive surface portion of the test sample according to any one of the second to thirty-second additional features and the electrical boundary of the electrically conductive surface portion y; ₂ ) determining,

(b) defining a fifth relationship comprising a fifteenth parameter indicative of said electrical characteristic and said additional distance y ₂ , and

and (c) determining said electrical property using said distance y ₂ in said fifth relation as said fifteenth parameter.

34. The 33rd further feature, wherein the fifth relation further comprises the spacing between the contact points of the first contact element, the second contact element, the third contact element, and / or the fourth contact element; ,

(b ') When defining the fifth relation, the fifth relation defines the distance between the contact points of the first contact element, the second contact element, the third contact element, and / or the fourth contact element. Further comprising a sixteenth parameter indicating,

(c ') In determining the electrical property, the interval is used as the sixteenth parameter in addition to the first distance y or the additional distance y ₂ in the fifth relation. Lt; / RTI >

35. The method of any one of the thirty-third additional feature and the thirty-fourth additional feature, wherein the electrical property is a hole sheet resistance R _H and the fifth relation f ₁ , f ₂ is an additional first resistance difference ΔR. _{BB ′} ) further comprises a seventeenth parameter, wherein the method includes:

(d) applying an additional first potential across the first and third contact elements to generate an additional first current in the surface portion at the first location,

(e) measuring the additional first current through the first or third contact element,

(f) measuring an additional first voltage across the second and fourth contact elements, and

(g) calculating an additional first resistance value R _B based on the additional first current and the additional first voltage, or

(g ') the step of retaining said first resistance value (R _B) from the step of determining the distance to the additional first resistance value (R _B), and

(h) applying an additional second potential across the second and fourth contact elements to generate an additional second current at the surface portion at the first location,

(i) measuring the additional second current through the second or fourth contact element,

(j) measuring an additional second voltage across the first and third contact elements, and

(k) calculating an additional second resistance value R _{B '} based on the additional second current and the additional second voltage, or

(k ') the step of retaining said second resistance value (R _B') from the step of determining the distance further second resistance value (R _{B 'to),} and

(l) calculating the additional first resistance difference ΔR _{BB ′} based on the difference between the additional first resistance value and the additional second resistance value, or

(l ') retaining the first resistance difference (R _{BB ′} ) from determining the distance as the additional first resistance difference (ΔR _{BB ′} ).

와 같고, 여기서 △R_BB'는 상기 추가적인 제1 저항차(△R_BB')를 나타내고, y는 상기 거리(y) 또는 상기 추가 거리를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내는 것을 특징으로 하는 방법.
36. The additional aspect 35, wherein the fifth relation is

ΔR _{BB ′} represents the additional first resistance difference ΔR _{BB ′} , and y represents the distance y or remind Represents an additional distance, a represents the spacing between the contact points of the first and second contact elements, b represents the spacing between the contact points of the second and third contact elements, and c is the third and fourth contacts A distance between the contact points of the elements.

37. The method of any one of the thirty-five additional features and the thirty-sixth additional features, wherein the electrical characteristic is a hole sheet resistance R _H and the fifth relation f ₂ , f ₃ is an additional second resistance difference ΔR _{CC '} ) further includes a seventeenth parameter, wherein the method includes:

(d) applying an additional third potential across the first and second contact elements to generate an additional third current at the surface portion at the first location,

(e) measuring the additional third current through the first or second contact element,

(f) measuring an additional third voltage across the third and fourth contact elements,

(g) calculating an additional third resistance value R _C based on the additional third current and the additional third voltage, or the steps (i.xii) to (i.xx) In the alternative,

(g ') the step of holding the third resistance value (R _C) from the step of determining the distance to an additional third resistance value (R _C),

(h) applying an additional fourth potential across the third and fourth contact elements to generate an additional fourth current in the surface portion at the first location,

(i) measuring the additional fourth current through the third or fourth contact element,

(j) measuring an additional fourth voltage across the first and second contact elements, and

(k) calculating an additional fourth resistance value R _{C ′} based on the additional fourth current and the additional fourth voltage, or remind Comprising steps (i.xii) to (i.xx) In the alternative,

(k ') retaining the fourth resistance value R _C' from determining the distance as an additional fourth resistance value R _{C '} , and

(l) calculating the additional second resistance difference ΔR _{CC ′} based on the difference between the additional third resistance value and the additional fourth resistance value, or Comprising steps (i.xii) to (i.xx) In the alternative,

(l '), characterized in that it comprises the step of holding said second resistance difference (△ R _CC') from the step of determining in the second additional resistance difference (△ R _CC the distance _") more.

와 같고, 여기서 △R_CC'는 상기 추가적인 제2 저항차(△R_CC')를 나타내고, y는 상기 거리(y) 또는 상기 추가 거리를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내는 것을 특징으로 하는 방법.
38. The additional aspect 37, wherein the fifth relation is

ΔR _{CC ′} represents the additional second resistance difference ΔR _{CC ′} , y represents the distance y or the additional distance, and a is the contact point of the first and second contact elements. Represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements. ≪ / RTI >

39. The method of any one of the thirty-third additional feature and the thirty-fourth additional feature, wherein the electrical property is a hole sheet resistance R _H and the fifth relation f ₁ is an additional third resistance difference ΔR _{AA ′} . Further comprising a seventeenth parameter, wherein the method,

(d) applying an additional fifth potential across the first and fourth contact elements to generate an additional fifth current at the surface portion at the first location,

(e) measuring the additional fifth current through the first or fourth contact element,

(f) measuring an additional fifth voltage across the second and third contact elements, and

(g) calculating an additional fifth resistance value R _A based on the additional fifth current and the additional fifth voltage, or

(g ') a step of holding the fifth resistance (R _A) from the step of determining the distance to an additional fifth resistance (R _A), and

(h) applying an additional sixth potential across the second and third contact elements to generate an additional sixth current in the surface portion at the first location,

(i) measuring the additional sixth current through the second or third contact element,

(j) measuring an additional sixth voltage across the first and fourth contact elements, and

(k) calculating an additional sixth resistance value R _{A '} based on the additional sixth current and the additional sixth voltage, or

(k ') holding the sixth resistance value R _A' from determining the distance as an additional fifth resistance value R _{A '} , and

(l) calculating the additional third resistance difference ΔR _{AA ′} based on the difference between the additional fifth resistance value and the additional sixth resistance value, or

(l '), characterized in that it comprises the step of holding the third resistance difference (△ R _AA') from the step of determining by said additional third resistance difference (△ R _AA the distance _") more.

와 같고, 여기서 △R_AA'는 상기 추가적인 제3 저항차(△R_AA')를 나타내고, y는 상기 거리(y) 또는 상기 추가 거리를 나타내고, a는 상기 제1 및 제2 접촉 요소의 접촉점들 간의 간격을 나타내고, b는 상기 제2 및 제3 접촉 요소의 접촉점들 간의 간격을 나타내며, c는 상기 제3 및 제4 접촉 요소의 접촉점들 간의 간격을 나타내는 것을 특징으로 하는 방법.
40. The additional feature of clause 39, wherein the fifth relational expression is

ΔR _{AA ′} represents the additional third resistance difference ΔR _{AA ′} , y represents the distance y or the additional distance, and a is the contact point of the first and second contact elements. The distance between them, b represents the distance between the contact points of the second and third contact elements, and c represents the distance between the contact points of the third and fourth contact elements.

41. The feature of any one of the thirty-third additional feature and the thirty-fourth additional feature, wherein the electrical characteristic is a sheet resistance R ₀ and the fifth relation g is a seventeenth parameter representing a pseudo sheet resistance R _P. Further comprising, the method,

(d) applying an additional fifth potential across the first and fourth contact elements to generate an additional fifth current at the surface portion at the first location,

(e) measuring the additional fifth current through the first or fourth contact element,

(f) measuring an additional fifth voltage across the second and third contact elements,

(g) calculating an additional fifth resistance value R _A based on the additional fifth current and the additional fifth voltage, or

(g ') a step of holding the fifth resistance (R _A) from the step of determining the distance to an additional fifth resistance (R _A), and

(h) applying an additional sixth potential across the second and third contact elements to generate an additional sixth current in the surface portion at the first location,

(i) measuring the additional sixth current through the second or third contact element,

(j) measuring an additional sixth voltage across the first and fourth contact elements,

(k) calculating an additional sixth resistance value R _{A '} based on the additional sixth current and the additional sixth voltage, or

(k ') holding the sixth resistance value R _A' from determining the distance as an additional fifth resistance value R _{A '} , and

)을 계산하는 단계, (l) a fifth resistance average of the additional fifth resistance value R _{A ′} and the additional sixth resistance value R _{A ′} (

),

(d ") applying an additional first potential across said first and third contact elements to generate an additional first current in said surface portion at said first location,

(e ") measuring said additional first current through said first or third contact element,

(f ") measuring an additional first voltage across said second and fourth contact elements,

(g ") calculating an additional first resistance value R _B based on said additional first current and said additional first voltage, or

(g ''') comprising: holding the first resistance value (R _B) from the step of determining the distance to the additional first resistance value (R _B), and

(h ") applying an additional second potential across said second and fourth contact elements to generate an additional second current in said surface portion at said first location,

(i ") measuring said additional second current through said second or fourth contact element,

(j ") measuring an additional second voltage across said first and third contact elements,

(k ″) calculating an additional second resistance value R _{B ′} based on the additional second current and the additional second voltage, or

(k ''') retaining the second resistance value R _B' from determining the distance as an additional second resistance value R _{B '} , and

)을 계산하는 단계, 및(l ″) a sixth resistance average of the additional first resistance value R _B and the additional second resistance value R _{B ′} (

), And

), 상기 제6 저항 평균(

), 및 상기 의사 시트 저항(R_P)을 각각 나타내는 제18, 제19, 및 제20 파라미터를 포함하는 제6 관계식을 정의하는 단계,(m) the fifth resistance average (

), The sixth resistance average (

), And defining a sixth relationship including the eighteenth, nineteenth, and twentieth parameters representing the pseudo sheet resistance R _P , respectively.

) 및 상기 제6 저항 평균(

)을 각각 상기 제18 파라미터 및 상기 제19 파라미터로서 이용하여 상기 의사 시트 저항(R_P)을 결정하는 단계를 더 포함하는 것을 특징으로 하는 방법.
(n) the fifth resistance average in the sixth equation (

) And the sixth resistance average (

) Determining the pseudo sheet resistance R _P using the eighteenth parameter and the nineteenth parameter, respectively.

와 같고, 여기서 R_P는 상기 의사 시트 저항이고,

는 상기 제1 저항 평균이며,

는 상기 제2 저항 평균인 것을 특징으로 하는 방법.
42. The additional feature of clause 41 wherein the sixth relation is

, Wherein R _P is the pseudo sheet resistance,

Is the first Resistance average,

Is the second A resistance average.

43. An apparatus for determining a distance between a first location on an electrically conductive surface portion of a test sample and an electrical boundary of the electrically conductive surface portion;

A multi additional point probe comprising a first contact element, a second contact element, a third contact element, and a fourth contact element, each contact element defining a contact point for establishing electrical contact with the test sample; and

Any of the first to thirty-second additional features A control unit configured to perform a method of determining the distance or an additional distance according to a feature

/ RTI >

44. An apparatus for determining electrical properties at a first location on an electrically conductive surface of a test sample, wherein

A multi additional point probe comprising a first contact element, a second contact element, a third contact element, and a fourth contact element, each contact element defining a contact point for establishing electrical contact with the test sample; and

An apparatus comprising a control unit configured to perform a method of determining electrical characteristics at a first location on an electrically conductive surface portion of the test sample according to any one of the 33rd to 42nd additional features.

12: second contact element
14: third contact element
16: fourth contact element
18: probe body
20: contact point of the first contact element
22: contact point of the second contact element
24: contact point of the third contact element
26: contact point of the fourth contact element
30: test sample
32: surface portion
33: Side
34: electrical boundaries
36: multi-point probe
40: common line
42: linear part
44: Electrically nonconductive surface
50-62: contact element
70-82: contact point
90: common line

Claims (48)

The distance between the first position on the electrically conducting surface portion of the test sample and the electrical boundary of the electrically conductive surface portion is determined by a first contact element, a second contact. A method of determining by a multi-point probe comprising an element, a third contact element, and a fourth contact element, each contact element having a contact point for establishing electrical contact with the test sample. )-,
(ii) the test sample with the first contact element, the second contact element, the third contact element, and the fourth contact element at the first location on the electrically conductive surface portion. Contacting,
(i.ii) applying a magnetic field having a major field component perpendicular to the electrically conductive surface portion at the first position,
(i.iii) applying a first electrical potential across the first and third contact elements to generate a first current in the surface portion at the first location,
(i.iv) passing through the first or third contact element Measuring the first current;
(iv) measuring a first voltage across the second and fourth contact elements,
(i.vi) calculating a first resistance value R _B based on the first current and the first voltage,
(i.vii) applying a second potential across the second and fourth contact elements to generate a second current in the surface portion at the first position,
(i.viii) measuring the second current through the second or fourth contact element,
(i.ix) measuring a second voltage across the first and third contact elements,
(ix) calculating a second resistance value R _{B ′} based on the second current and the second voltage,
(i.xi) calculating a first resistance difference ΔR _{BB ′} based on a difference between the first resistance value and the second resistance value,
(i.xii) applying a third potential across the first and second contact elements to generate a third current in the surface portion at the first location,
(i.xiii) measuring the third current through the first or second contact element,
(i.xiv) measuring a third voltage across the third and fourth contact elements,
(i.xv) calculating a third resistance value R _C based on the third current and the third voltage,
(i.xvi) applying a fourth potential across the third and fourth contact elements to generate a fourth current in the surface portion at the first position,
(i.xvii) measuring the fourth current through the third or fourth contact element,
(i.xviii) measuring a fourth voltage across the first and second contact elements,
(i.xix) calculating a fourth resistance value R _{C ′} based on the fourth current and the fourth voltage,
(i.xx) calculating a second resistance difference ΔR _{CC ′} based on the difference between the third resistance value and the fourth resistance value,
(i.xxi) A first relation f comprising first, second, and third parameters representing the first resistance difference, the second resistance difference, and the distance between the first position and the electrical boundary, respectively. ), And
(i.xxii) wherein the using in the first equation of the first and second resistance difference _{(△ R BB ', △ R} CC', △ R BB ', 2) to each of the first and a second parameters Determining the third parameter representing the distance y between one location and the electrical boundary
≪ / RTI > The distance between the first position on the electrically conducting surface portion of the test sample and the electrical boundary of the electrically conductive surface portion is determined by a first contact element, a second contact. A method of determining by a multi-point probe comprising an element, a third contact element, and a fourth contact element, each contact element having a contact point for establishing electrical contact with the test sample. )-,
(ii) contacting the test sample with the first contact element, the second contact element, the third contact element, and the fourth contact element at the first location on the electrically conductive surface portion,
(i.ii) applying a magnetic field having a field component perpendicular to the electrically conductive surface portion at the first position,
(i.iii) applying a first electrical potential across the first and third contact elements to generate a first current in the surface portion at the first location,
(i.iv) measuring the first current through the first or third contact element,
(iv) measuring a first voltage across the second and fourth contact elements,
(i.vi) calculating a first resistance value R _B based on the first current and the first voltage,
(i.vii) applying a second potential across the second and fourth contact elements to generate a second current in the surface portion at the first position,
(i.viii) measuring the second current through the second or fourth contact element,
(i.ix) measuring a second voltage across the first and third contact elements,
(ix) calculating a second resistance value R _{B ′} based on the second current and the second voltage,
(i.xi) calculating a first resistance difference ΔR _{BB ′} based on the difference between the first resistance value and the second resistance value, wherein the multi-point probe includes a plurality of contact elements, and The plurality of contact elements includes the first contact element, the second contact element, the third contact element, the fourth contact element and one or more additional contact elements, each of the one or more additional contact elements being associated with the test sample. Defines a contact point for establishing electrical contact with
(ii.xii) defining a contact element of a first configuration of the plurality of contact elements, wherein the contact element of the first configuration comprises the first contact element, the second contact element, the third contact element, and the Consisting of the fourth contact element-,
(ii.xiii) defining a contact element of a second configuration of the plurality of contact elements, wherein the contact element of the second configuration is a fifth contact element, a sixth contact element, a seventh contact element, and an eighth contact element. Wherein at least one of the contact elements of the second configuration is a contact element of the one or more additional contact elements,
(ii.xiv) contacting said test sample with said contact element of said second configuration at said first location on said electrically conductive surface portion while simultaneously bringing said test sample into said contact element of said first configuration; Contacting with the contact element,
(ii.xv) applying a third potential across the fifth and seventh contact elements to generate a third current in the surface portion at the first position,
(ii.xvi) measuring the third current through the fifth or seventh contact element,
(ii.xvii) measuring a third voltage across the sixth and eighth contact elements,
(ii.xviii) calculating a third resistance value R _{B , 2} based on the third current and the third voltage,
(ii.xix) applying a fourth potential across the sixth and eighth contact elements to generate a fourth current in the surface portion at the first position,
(ii.xx) measuring the fourth current through the sixth or eighth contact element,
(ii.xxi) measuring a fourth voltage across the fifth and seventh contact elements,
(ii.xxii) calculating a fourth resistance value R _{B ′ , 2} based on the fourth current and the fourth voltage,
(ii.xxiii) calculating a second resistance difference ΔR _{BB ′ , 2} based on the difference between the third resistance value and the fourth resistance value,
(i.xxi) A first relation f comprising first, second, and third parameters representing the first resistance difference, the second resistance difference, and the distance between the first position and the electrical boundary, respectively. ), And
(i.xxii) wherein the using in the first equation of the first and second resistance difference _{(△ R BB ', △ R} CC', △ R BB ', 2) to each of the first and a second parameters Determining the third parameter representing the distance y between one location and the electrical boundary
≪ / RTI > 3. The method of claim 2,
(iii.xxiv) a first average resistance of the first resistance value (R _B) and said second resistance value (R _{B ')} (

),
(iii.xxv) a second resistance average of the third resistance value R _{B , 2} and the fourth resistance value R _{B ′ , 2} ;

),
(iii.xxvi) applying a fifth potential across the first and fourth contact elements to generate a fifth current in the surface portion at the first location,
(iii.xxvii) measuring the fifth current through the first or fourth contact element,
(iii.xxviii) measuring a fifth voltage across the second and third contact elements,
(iii.xxix) calculating a fifth resistance value R _{A , 1} based on the fifth current and the fifth voltage,
(iii.xxx) applying a sixth potential across the second and third contact elements to generate a sixth current in the surface portion at the first location,
(iii.xxxi) measuring the sixth current through the second or third contact element,
(iii.xxxii) measuring a sixth voltage across the first and fourth contact elements,
(iii.xxxiii) calculating a sixth resistance value R _{A ′ , 1} based on the sixth current and the sixth voltage,
(iii.xxxiv) a third resistance average of the fifth resistance value R _{A , 1} and the sixth resistance value R _{A ′ , 1} ;

),
(iii.xxxv) applying a seventh potential across the fifth and eighth contact elements to generate a seventh current in the surface portion at the first position,
(iii.xxxvi) measuring the seventh current through the fifth or eighth contact element,
(iii.xxxvii) measuring a seventh voltage across the sixth and seventh contact elements,
(iii.xxxviii) calculating a seventh resistance value R _{A , 2} based on the seventh current and the seventh voltage,
(iii.xxxix) applying an eighth potential across the sixth and seventh contact elements to generate an eighth current in the surface portion at the first position,
(iii.xl) measuring the eighth current through the sixth or seventh contact element,
(iii.xli) measuring an eighth voltage across the fifth and eighth contact elements,
(iii.xlii) calculating an eighth resistance value R _{A ′ , 2} based on the eighth current and the eighth voltage,
(iii.xliii) a fourth resistance average of the seventh resistance value R _{A , 2} and the eighth resistance value R _{A ′ , 2} (

),
(iii.xliv) the first resistance average (

), The third resistance average (

) And a second relationship comprising fourth, fifth, and sixth parameters representing the _first pseudo sheet resistance R _{P , 1} , respectively,
(iii.xlv) the average of the first resistance in the second relation (

) And the third resistance average (

Determining each of the sixth parameters representing the first pseudo sheet resistance R _{P , 1 using} R as the fourth parameter and the fifth parameter, respectively.
(iii.xlvi) the second resistance average (

), The fourth resistance average (

), And defining a third relationship comprising seventh, eighth, and ninth parameters representing the second pseudo sheet resistance R _{P , 2} , respectively,
(iii.xlvii) the second resistance mean in the third relation

) And the fourth resistance average (

Determining the ninth parameter representing the second pseudo sheet resistance R _{P , 2} using each of the seventh parameter and the eighth parameter,
(iii.xlviii) the tenth and the third representing the first pseudo sheet resistance R _{P , 1} , the second pseudo sheet resistance R _{P , 2} , and the distance between the first position and the electrical boundary, respectively. Defining a fourth relation g _D comprising 11, and a twelfth parameter, and
(iii.xlix) the first position using the first and second pseudo sheet resistances R _{P , 1} , R _{P, 2 as} the tenth and eleventh parameters, respectively _{, in} the fourth relation g _D ; Determining the twelfth parameter indicative of an additional distance y ₂ between the electrical boundary and the electrical boundary.
To To include more Lt; / RTI > The method of claim 3, wherein the fourth relation is equal to R _{P , 1} / R _{P , 2} = g _D (y), wherein R _{P , 1} represents the first pseudo sheet resistance, and R _{P , 2} represents the above Represents a second pseudo sheet resistance, g _D represents a function comprising the distance y as a parameter, the function g _D defines a peak value at a specific distance, and the function g _D is a function of the distance Increases when it is below and decreases when the function of the distance exceeds the specific distance,
The method comprises:
(iii.xlx) comparing the distance with the specific distance to determine whether the additional distance is less than or greater than the specific distance in the fourth relationship. 3. The method of claim 2,
(iii.xxiv) a first average resistance of the first resistance value (R _B) and said second resistance value (R _{B ')} (

),
(iii.xxv) a second resistance average of the third resistance value R _{B , 2} and the fourth resistance value R _{B ′ , 2} ;

),
(iii.xxvi) applying a fifth potential across the first and fourth contact elements to generate a fifth current in the surface portion at the first location,
(iii.xxvii) measuring the fifth current through the first or fourth contact element,
(iii.xxviii) measuring a fifth voltage across the second and third contact elements,
(iii.xxix) calculating a fifth resistance value R _{A , 1} based on the fifth current and the fifth voltage,
(iii.xxx) applying a sixth potential across the second and third contact elements to generate a sixth current in the surface portion at the first location,
(iii.xxxi) measuring the sixth current through the second or third contact element,
(iii.xxxii) measuring a sixth voltage across the first and fourth contact elements,
(iii.xxxiii) calculating a sixth resistance value R _{A ′ , 1} based on the sixth current and the sixth voltage,
(iii.xxxiv) a third resistance average of the fifth resistance value R _{A , 1} and the sixth resistance value R _{A ′ , 1} ;

),
(iii.xxxv) applying a seventh potential across the fifth and eighth contact elements to generate a seventh current in the surface portion at the first position,
(iii.xxxvi) measuring the seventh current through the fifth or eighth contact element,
(iii.xxxvii) measuring a seventh voltage across the sixth and seventh contact elements,
(iii.xxxviii) calculating a seventh resistance value R _{A , 2} based on the seventh current and the seventh voltage,
(iii.xxxix) applying an eighth potential across the sixth and seventh contact elements to generate an eighth current in the surface portion at the first position,
(iii.xl) measuring the eighth current through the sixth or seventh contact element,
(iii.xli) measuring an eighth voltage across the fifth and eighth contact elements,
(iii.xlii) calculating an eighth resistance value R _{A ′ , 2} based on the eighth current and the eighth voltage,
(iii.xliii) a fourth resistance average of the seventh resistance value R _{A , 2} and the eighth resistance value R _{A ′ , 2} (

),
(iii.xliv) the first resistance average (

), The third resistance average (

) And a second relationship comprising fourth, fifth, and sixth parameters representing the _first pseudo sheet resistance R _{P , 1} , respectively,
(iii.xlv) the average of the first resistance in the second relation (

) And the third resistance average (

Determining each of the sixth parameters representing the first pseudo sheet resistance R _{P , 1 using} R as the fourth parameter and the fifth parameter, respectively.
(iii.xlvi) the second resistance average (

), The fourth resistance average (

), And defining a third relationship comprising seventh, eighth, and ninth parameters representing the second pseudo sheet resistance R _{P , 2} , respectively,
(iii.xlvii) the second resistance mean in the third relation

) And the fourth resistance average (

Determining the ninth parameter representing the second pseudo sheet resistance R _{P , 2} using each of the seventh parameter and the eighth parameter, and
(iii.xlviii) the tenth and the third representing the first pseudo sheet resistance R _{P , 1} , the second pseudo sheet resistance R _{P , 2} , and the distance between the first position and the electrical boundary, respectively. Defining a fourth relation g _D comprising an eleventh, and a twelfth parameter, wherein the contact element of the second configuration comprises the electrically conductive surface portion and the electrically conductive surface portion of the test sample; An additional distance y ₂ between electrical boundaries, the first relation f _D further comprises a thirteenth parameter representing the additional distance between the first position and the electrical boundaries, and the fourth relation g _D ) Further comprises a fourteenth parameter representing the additional distance between the first location and the electrical boundary.
Further comprising:
The method comprises:
(iv.xlix) the first position using the first and second pseudo sheet resistances R _{P , 1} , R _{P, 2 as} the tenth and eleventh parameters, respectively _{, in} the fourth relation g _D ; And simultaneously determining the thirteenth parameter and the fourteenth parameter representing the distance y and the additional distance y ₂ between the electrical boundary, respectively. The distance between the first position on the electrically conducting surface portion of the test sample and the electrical boundary of the electrically conductive surface portion is multi-containing a plurality of contact elements. Method determined by multi-point probe, each contact element defining a contact point for establishing electrical contact with the test sample, wherein the plurality of contact elements comprise a first contact element, a first contact element A second contact element, a third contact element, a fourth contact element and one or more additional contact elements, wherein
(vi) defining a contact element of a first configuration of the plurality of contact elements, wherein the contact element of the first configuration comprises the first contact element, the second contact element, the third contact element, and the fourth contact element; Consisting of contact elements-,
(v.ii) defining a contact element of a second configuration of the plurality of contact elements, wherein the contact element of the second configuration comprises a fifth contact element, a sixth contact element, a seventh contact element, and an eighth contact element; Wherein at least one of the contact elements of the second configuration is a contact element of the one or more additional contact elements,
(v.iii-iv) contacting the test sample with the contact element of the contact element of the first and second configurations at the first location on the electrically conductive surface portion,
(vv) applying a magnetic field having a main field component perpendicular to the electrically conductive surface portion at the first location,
(v.vi) applying a first potential across the first and third contact elements to generate a first current in the surface portion at the first location,
(v.vii) measuring the first current through the first or third contact element,
(v.viii) measuring a first voltage across the second and fourth contact elements,
(v.ix) calculating a first resistance value R _B based on the first current and the first voltage,
(vx) applying a second potential across the second and fourth contact elements to generate a second current in the surface portion at the first position,
(v.xi) measuring the second current through the second or fourth contact element,
(v.xii) measuring a second voltage across the first and third contact elements,
(v.viii) calculating a second resistance value R _{B ′} based on the second current and the second voltage,
(v.xiv) a first average resistance of the first resistance value (R _B) and said second resistance value (R _{B ')} (

),
(v.xv) applying a third potential across the fifth and seventh contact elements to generate a third current at the surface portion at the first position,
(v.xvi) measuring the third current through the fifth or seventh contact element,
(v.xvii) measuring a third voltage across the sixth and eighth contact elements,
(v.xviii) calculating a third resistance value R _{B , 2} based on the third current and the third voltage,
(v.xix) applying a fourth potential across the sixth and eighth contact elements to generate a fourth current in the surface portion at the first position,
(v.xx) measuring the fourth current through the sixth or eighth contact element,
(v.xxi) measuring a fourth voltage across the fifth and seventh contact elements,
(v.xxii) calculating a fourth resistance value R _{B ′ , 2} based on the fourth current and the fourth voltage,
(v.xxv) A second resistance average of the third resistance value R _{B , 2} and the fourth resistance value R _{B ′ , 2} (

),
(v.xxvi) applying a fifth potential across the first and fourth contact elements to generate a fifth current in the surface portion at the first location,
(v.xxvii) measuring the fifth current through the first or fourth contact element,
(v.xxviii) measuring a fifth voltage across the second and third contact elements,
(v.xxix) calculating a fifth resistance value R _{A , 1} based on the fifth current and the fifth voltage,
(v.xxx) applying a sixth potential across the second and third contact elements to generate a sixth current in the surface portion at the first location,
(v.xxxi) measuring the sixth current through the second or third contact element,
(v.xxxii) measuring a sixth voltage across the first and fourth contact elements,
(v.xxxiii) calculating a sixth resistance value R _{A ′ , 1} based on the sixth current and the sixth voltage,
(v.xxxiv) a third resistance average of the fifth resistance value R _{A , 1} and the sixth resistance value R _{A ′ , 1}

),
(v.xxxv) applying a seventh potential across the fifth and eighth contact elements to generate a seventh current in the surface portion at the first position,
(v.xxxvi) measuring the seventh current through the fifth or eighth contact element,
(v.xxxvii) measuring a seventh voltage across the sixth and seventh contact elements,
(v.xxxviii) calculating a seventh resistance value R _{A , 2} based on the seventh current and the seventh voltage,
(v.xxxix) applying an eighth potential across the sixth and seventh contact elements to generate an eighth current in the surface portion at the first position,
(v.xl) measuring the eighth current through the sixth or seventh contact element,
(v.xli) measuring an eighth voltage across the fifth and eighth contact elements,
(v.xlii) calculating an eighth resistance value R _{A ′ , 2} based on the eighth current and the eighth voltage,
(v.xliii) a fourth resistance average of the seventh resistance value R _{A , 2} and the eighth resistance value R _{A ′ , 2} (

),
(v.xliv) the first resistance average (

), The third resistance average (

) And a second relationship comprising fourth, fifth, and sixth parameters representing the _first pseudo sheet resistance R _{P , 1} , respectively,
(v.xlv) the first resistance average in the second relation

) And the third resistance average (

Determining each of the sixth parameters representing the first pseudo sheet resistance R _{P , 1 using} R as the fourth parameter and the fifth parameter, respectively.
(v.xlvi) the second resistance average (

), The fourth resistance average (

), And defining a third relationship comprising seventh, eighth, and ninth parameters representing the second pseudo sheet resistance R _{P , 2} , respectively,
(v.xlvii) the second resistance average in the third relation

) And the fourth resistance average (

Determining the ninth parameter representing the second pseudo sheet resistance R _{P , 2} using each of the seventh parameter and the eighth parameter,
(v.xlviii) the tenth and the fifth representing the first pseudo sheet resistance R _{P , 1} , the second pseudo sheet resistance R _{P , 2} , and the distance between the first position and the electrical boundary, respectively. Defining a fourth relation g _D comprising 11, and a twelfth parameter, and
(v.xlix) the first position using the first and second pseudo sheet resistances R _{P , 1} , R _{P, 2 as} the tenth and eleventh parameters, respectively _{, in} the fourth relation g _D ; Determining the twelfth parameter indicative of the value of the distance y between the electrical boundary and the electrical boundary.
≪ / RTI > The method of claim 6, wherein the fourth relation is R _{P , 1} / R _{P , 2} = g _D (y) and Wherein R _{P , 1} represents the first pseudo sheet resistance, R _{P , 2} represents the second pseudo sheet resistance, g _D represents a function including the distance y as a parameter, and the function g _D Denotes a peak value at a specific distance, and the function g _D is when the function of the distance is less than the specific distance Increase and decrease when the function of the distance exceeds the specific distance,
The method comprises:
(v.xlx) determining a distance indicative of an auxiliary distance by a method according to any one of claims 1 to 5, and
(v.xlxi) further comprising comparing the auxiliary distance with the specific distance and determining whether the distance is less than or greater than the specific distance in the fourth relational expression. 8. The method of claim 1, wherein the contact point defines a first line that intersects each of the contact points. 9. The method of claim 2, wherein the first contact element, the second contact element, the third contact element, the fourth contact element, and the contact point before the contact point contacts the test sample. Said at least one further contact element And a first line defining a contact point intersecting each said contact point. The contact point of claim 9, wherein the contact points of the first contact element, the second contact element, the third contact element, and the fourth contact element are in a given order along the first line. And arranged. The method of claim 10, wherein the contact points of the fifth contact element, the sixth contact element, the seventh contact element, and the eighth contact element are disposed along the first line in a given order. . The method of claim 10, wherein the spacing between the first and second contact elements, the second and third contact elements, and the contact points of the third and fourth contact elements is approximately zero. Equal to 1 interval value (s ₁ ) ≪ / RTI > The method of claim 10, wherein the spacing between the fifth and sixth contact elements, the sixth and seventh contact elements, and the contact elements of the seventh and eighth contact elements is approximately. And a second interval value s ₂ . The method of claim 13, wherein the first relation is equal to _{ΔR BB ′} / ΔR _{BB ′ , 2} = f _D (y, s ₁ , s ₂ ), wherein ΔR _{BB ′} represents the first resistance difference. _{ΔR BB′2} represents the second resistance difference, and f _D includes the distance y between the first position and the electrical boundary, the first interval value s ₁ , and the second interval value s ₂ Method, characterized in that the function. The function f _D (y, s ₁ , s ₂ ) in the first relation ΔR _{BB ′} / ΔR _{BB ′ , 2} = f _D (y, s ₁ , s ₂ )

And characterized in that. The method of claim 3, wherein the second relational expression is

Wherein R _{P , 1} represents the first pseudo sheet resistance,

Is the first resistance average,

Is the third resistance average, and the third relational expression is

, Wherein R _{P, 2} is the second pseudo sheet resistance,

Is the second resistance average,

Is the fourth resistance average. Claim 1 according to claim 3 or 3 17. The method of any one of claims 16 to 18, wherein the fourth relation is equal to R _{P , 1} / R _{P , 2} = g _D (y, s ₁ , s ₂ ), wherein R _{P , 1} is the first pseudo Sheet resistance, R _{P , 2} represents the second pseudo sheet resistance, g _D is the distance y between the first position and the electrical boundary, the first spacing value s ₁ , and the second spacing value s _And a function comprising a _two . Claim 1 according to claim 5 or 5 The method according to any one of claims 17 to 17, wherein the first relational formula is equal to _{ΔR BB ′} / ΔR _{BB ′ , 2} = f _D (y, y ₂ , s ₁ , s ₂ ), wherein ΔR _{BB ′} Denotes the first resistance difference, ΔR _{BB ′ , 2} denotes the second resistance difference, f _D denotes the distance y and the additional distance y ₂ between the first position and the electrical boundary, and the first interval A function comprising a value s ₁ and the second interval value s ₂ . The method according to claim 18, wherein the function f _D (y, y ₂ , s ₁ ,) in the first relation ΔR _{BB ′} / ΔR _{BB ′ , 2} = f _D (y, y ₂ , s ₁ , s ₂ ) s ₂ ) is

And characterized in that. Claim 1 according to claim 5 or 5 20. The method of any one of claims 19 to 20, wherein the fourth relation is equal to R _{P , 1} / R _{P , 2} = g _D (y, y ₂ , s ₁ , s ₂ ), wherein R _{P , 1} is 1 represents a pseudo sheet resistance, R _{P , 2} represents the second pseudo sheet resistance, g _D is the distance y between the first position and the electrical boundary and the additional distance y ₂ , the first spacing value s ₁ And a second interval value s ₂ . 21. The electrical boundary of any one of claims 8 to 20, wherein the electrical boundary has an approximately linear portion and the distance between the first position and the additional point on the linear portion is the electrical boundary outside the first position and the linear portion. Shorter than the distance between any additional points on the image. The method of claim 21,
(vi.i) orienting the multi-point probe to be in the first line in a parallel relationship with the linear portion. 23. The method of any one of claims 1 to 22, wherein the spacing between the first and second contact elements, the second and third contact elements, and the connection points of the third and fourth contact elements are approximately equal. Characterized in that the method. Claim 1 dependent on claims 23 and 1 The method according to any one of claims 23 to 23, wherein the first relational expression is equal to _{ΔR CC ′} / ΔR _{BB ′} = f (y, s), wherein ΔR _{BB ′} represents the first resistance difference, Δ R _{CC '} represents the second resistance difference, and f is a function comprising as a parameter the distance y between the first position and the electrical boundary and the spacing s between the contact points. 25. The method of claim 24, wherein in the relation ΔR _{CC '} / ΔR _BB' = f (y, s), the first resistance difference ΔR _{BB '} is

ΔR _{B B ′} represents the additional first resistance difference ΔR _{BB ′} , y represents the distance y, and a is the spacing between the contact points of the first and second contact elements. B denotes an interval between the contact points of the second and third contact elements, c denotes an interval between the contact points of the third and fourth contact elements, and the relation ΔR _{CC ′} / ΔR _{BB ′} At f (y, s), the second resistance difference ΔR _{CC ′} is

ΔR _{C C ′} represents the additional second resistance difference ΔR _{CC ′} , y represents the distance y, and a is the spacing between the contact points of the first and second contact elements. And b represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements. Section 1 or Claim 1 dependent on claim 1 The method according to any one of claims 25 to 25,
(i.xxiii) applying a fifth potential across the first and fourth contact elements to generate a fifth current in the surface portion at the first location,
(i.xxiv) measuring the fifth current through the first or fourth contact element,
(i.xxv) measuring a fifth voltage across the second and third contact elements,
(i.xxvi) calculating a fifth resistance value R _A based on the fifth current and the fifth voltage,
(i.xxvii) applying a sixth potential across the second and third contact elements to generate a sixth current in the surface portion at the first location,
(i.xxviii) measuring the sixth current through the second or third contact element,
(i.xxix) measuring a sixth voltage across the first and fourth contact elements,
(i.xxx) calculating a sixth resistance value R _{A ′} based on the sixth current and the sixth voltage,
(i.xxxi) calculating a third resistance difference ΔR _{AA ′} based on the difference between the fifth resistance value and the sixth resistance value,
(i.xxxii) when defining the first relation f, further including a fourth parameter representing the third resistance difference ΔR _{AA ′ in} the first relation f, and
(i.xxxiii) when determining the distance y between the first position and the electrical boundary, the first and second resistance differences used as the first and second parameters, respectively, in the first relational expression ( Using the third resistance difference ΔR _{AA ′} as the fourth parameter in addition to ΔR _{BB ′} and ΔR _{CC ′} ). It further comprises a method. 27. The device of claim 1, wherein the contact points are disposed in-line, the spacing between the contact points of the first and second contact elements and the second and third contact elements. The spacing between the contact points of is about equal ≪ / RTI > 28. The device of any one of claims 1 to 27, wherein the contact points are arranged in line and the spacing between the contact points of the third and fourth contact elements is between the contact points of the first and second contact elements. Method characterized by being different from the interval. The method of claim 28, wherein the spacing between the contact points of the third and fourth contact elements is greater than the spacing between the contact points of the first and second contact elements. One or more of the ranges 1.1-3.7, 1.2-3.3, 1.3-2.9, 1.4-2.5, 1.5-2.1, and 1.6-1.7, and / or the ranges 1.2-1.3, 1.3-1.4, 1.4-1.5, 1.5-1.6, 1.6 Factor within one of -1.7, 1.7-1.8, 1.8-1.9, 1.9-2.0, 2.0-2.2, 2.2-2.4, 2.4-2.6, 2.6-2.8, 2.8-3.0, 3.0-3.3, 3.3-3.6, 3.6-3.9 , And / or approximately 5 divided by 3, or one or more of the ranges 1.2-3.8, 1.6-3.4, 1.8-3.2, 2.0-3.0, 2.2-2.8, and 2.4-2.6, and / or the range 1.2-1.3, 1.3-1.4, 1.4-1.5, 1.5-1.6, 1.6-1.7, 1.7-1.8, 1.8-1.9, 1.9-2.0, 2.0-2.2, 2.2-2.4, 2.4-2.6, 2.6-2.8, 2.8-3.0, 3.0- A factor within one of 3.3, 3.3-3.6, 3.6-3.9, and / or approximately as large as two divided by two. 30. The method of any one of the preceding claims, wherein the spacing between the contact points of the first and second contact elements is One of the ranges 1-5 μm, 5-10 μm, 10-15 μm, 15-20 μm, 20-25 μm, 25-30 μm, 30-40 μm, 40-50 μm, 50-500 μm, and / Or in the range 1-50 μm, 5-40 μm, 10-30 μm, 15-25 μm. 31. The method of any one of claims 26 to 30, wherein the first relation is equal to (ΔR _{AA ′} + αΔR _{CC ′} ) / ΔR _{BB ′} = f (y, a, b, c) Where ΔR _{BB ′} is the first resistance difference, ΔR _{CC ′} is the second resistance difference, ΔR _{AA ′} is the third resistance difference, and α is a tuning factor in the range of −10 to 10. F is a function including the distance y between the first position and the electrical boundary, a is the spacing between the contact points of the first and second contact elements, and b is the second and third contacts The spacing between the contact points of the element, and c is the spacing between the contact points of the third and fourth contact elements. 32. The method of claim 31, wherein the tuning factor α is approximately 1 or approximately -1. 32. The method of any one of claims 30 and 31, wherein the first resistance difference in the relation (ΔR _{AA ′} + αΔR _{CC ′} ) / ΔR _{BB ′} = f (y, a, b, c). △ R _{BB '} is

ΔR _{BB ′} represents the additional first resistance difference ΔR _{AA ′} , y represents the distance y, and a represents the distance between the contact points of the first and second contact elements. B denotes the spacing between the contact points of the second and third contact elements, c denotes the spacing between the contact points of the third and fourth contact elements, and the relationship (ΔR _{AA ′} + αΔR _{CC) '} ) / ΔR _BB' = f (y, a, b, c), the second resistance difference ΔR _{CC '} is

ΔR _{CC ′} represents the additional second resistance difference ΔR _{CC ′} , y represents the distance y, and a represents the distance between the contact points of the first and second contact elements. B denotes the spacing between the contact points of the second and third contact elements, c denotes the spacing between the contact points of the third and fourth contact elements, and the relationship (ΔR _{AA ′} + αΔR _{CC) '} ) / ΔR _BB' = f (y, a, b, c), the third resistance difference ΔR _{AA '} is

ΔR _{A A ′} represents the additional third resistance difference ΔR _{AA ′} , y represents the distance y, and a is the spacing between the contact points of the first and second contact elements. And b represents the spacing between the contact points of the second and third contact elements, and c represents the spacing between the contact points of the third and fourth contact elements. 34. The method of any one of claims 1 to 33, wherein the spacing between the contact points of the first and second contact elements is in the range 0.1-100 µm, 1-90 µm, 10-80 µm, 20-70 µm. At least one of 30-60 μm, and 40-50 μm, and / or range 0.1-1 μm, 1-10 μm, 10-20 μm, 20-30 μm, 30-40 μm, 40-50 μm, 50 And within one of -60 μm, 60-70 μm, 70-80 μm, 80-90 μm, 90-100 μm, or 100-500 μm. A method for determining electrical properties at a first location on an electrically conducting surface portion of a test sample, the electrically conductive surface portion having an electrical boundary.
(a) the above claim according to any one of claims 1 to 34, wherein The electrically conductive of the test sample Determining a distance y between the first location on the surface portion and the electrical boundary of the electrically conductive surface portion,
(b) defining a fifth relational expression comprising a fifteenth parameter indicative of said electrical characteristic and said distance y, and
(c) determining the electrical property using the distance y as the fifteenth parameter in the fifth relationship
≪ / RTI > A method for determining electrical properties at a first location on an electrically conducting surface portion of a test sample, the electrically conductive surface portion having an electrical boundary.
(a) paragraph 2 Or claim 1 according to any one of claims 6 or 2 or 6. Determining an additional distance y ₂ between said first location on said electrically conductive surface portion of said test sample and said electrical boundary of said electrically conductive surface portion,
(b) defining a fifth relationship comprising a fifteenth parameter indicative of said electrical characteristic and said additional distance y ₂ , and
(c) determining the electrical property using the additional distance y ₂ as the fifteenth parameter in the fifth relational equation.
≪ / RTI > 37. The method of claim 35 or 36, wherein the fifth relation further comprises the spacing between the contact points of the first contact element, the second contact element, the third contact element, and / or the fourth contact element. and,
(b ') When defining the fifth relation, the fifth relation defines the distance between the contact points of the first contact element, the second contact element, the third contact element, and / or the fourth contact element. Further comprising a sixteenth parameter indicating,
(c ') In determining the electrical property, the interval is used as the sixteenth parameter in addition to the first distance y or the additional distance y ₂ in the fifth equation. 38. The electrical property of any one of claims 35 to 37 wherein the electrical property is a Hall sheet resistance (R _H ) and the fifth relation (f ₁ , f ₂ ) is an additional first resistance difference ΔR. _{BB '} ) further includes a seventeenth parameter,
The method comprises:
(d) applying an additional first potential across the first and third contact elements to generate an additional first current in the surface portion at the first location,
(e) measuring the additional first current through the first or third contact element,
(f) measuring an additional first voltage across the second and fourth contact elements, and
(g) calculating an additional first resistance value R _B based on the additional first current and the additional first voltage, or
(g ') the step of retaining said first resistance value (R _B) from the step of determining the distance to the additional first resistance value (R _B), and
(h) applying an additional second potential across the second and fourth contact elements to generate an additional second current at the surface portion at the first location,
(i) measuring the additional second current through the second or fourth contact element,
(j) measuring an additional second voltage across the first and third contact elements, and
(k) calculating an additional second resistance value R _{B '} based on the additional second current and the additional second voltage, or
(k ') the step of retaining said second resistance value (R _B') from the step of determining the distance further second resistance value (R _{B 'to),} and
(l) calculating the additional first resistance difference ΔR _{BB ′} based on the difference between the additional first resistance value and the additional second resistance value, or
(l ') holding the first resistance difference ΔR _{BB ′} from determining the distance as the additional first resistance difference _{ΔR BB ′} .
≪ / RTI > The method of claim 38,
The fifth relationship is

ΔR _{BB ′} represents the additional first resistance difference ΔR _{BB ′} , and y represents the distance y or The additional distance, a denotes the spacing between the contact points of the first and second contact elements, b denotes the spacing between the contact points of the second and third contact elements, and c denotes the third and fourth And a distance between the contact points of the contact elements. Article 35 And The method according to any one of claims 37 to 39, wherein
The electrical property is a Hall sheet resistance (R _H ) and the fifth relation (f ₂ , f ₃ ) further includes a seventeenth parameter representing an additional second resistance difference ΔR _{CC ′} ,
The method comprises:
(d) applying an additional third potential across the first and second contact elements to generate an additional third current at the surface portion at the first location,
(e) measuring the additional third current through the first or second contact element,
(f) measuring an additional third voltage across the third and fourth contact elements,
(g) calculating an additional third resistance value R _C based on the additional third current and the additional third voltage, or
(g ') the step of holding the third resistance value (R _C) from the step of determining the distance to an additional third resistance value (R _C), and
(h) applying an additional fourth potential across the third and fourth contact elements to generate an additional fourth current in the surface portion at the first location,
(i) measuring the additional fourth current through the third or fourth contact element,
(j) measuring an additional fourth voltage across the first and second contact elements, and
(k) calculating an additional fourth resistance value R _{C ′} based on the additional fourth current and the additional fourth voltage, or
(k ') the step of holding the fourth resistance (R _C') from the step of determining the distance further the fourth resistance (R _{C 'to),} and
(l) calculating the additional second resistance difference ΔR _{CC ′} based on the difference between the additional third resistance value and the additional fourth resistance value, or
(l ') the step of holding said second resistance difference (△ R _CC') from the step of determining in the second additional resistance difference (△ R _CC the distance _")
≪ / RTI > Section 3 6 And 40. The electrical property of any of claims 37 to 39, wherein the electrical property is a hole sheet resistance (R _H ) and the fifth relation (f ₂ , f ₃ ) is an additional second resistance difference ( Further comprising a seventeenth parameter representing _{ΔR CC ′} ),
The method comprises:
(d) applying an additional third potential across the first and second contact elements to generate an additional third current at the surface portion at the first location,
(e) measuring the additional third current through the first or second contact element,
(f) measuring an additional third voltage across the third and fourth contact elements,
(g) calculating an additional third resistance value R _C based on the additional third current and the additional third voltage,
(h) applying an additional fourth potential across the third and fourth contact elements to generate an additional fourth current in the surface portion at the first location,
(i) measuring the additional fourth current through the third or fourth contact element,
(j) measuring an additional fourth voltage across the first and second contact elements,
(k) calculating an additional fourth resistance value R _{C ′} based on the additional fourth current and the additional fourth voltage, and
(l) calculating the additional second resistance difference ΔR _{CC ′} based on the difference between the additional third resistance value and the additional fourth resistance value. 42. The method of claim 40 or 41 wherein the fifth relational formula is

ΔR _{CC ′} represents the additional second resistance difference ΔR _{CC ′} , y represents the distance y or the additional distance, and a is the contact point of the first and second contact elements. The distance between them, b represents the distance between the contact points of the second and third contact elements, and c represents the distance between the contact points of the third and fourth contact elements. 37. The method of any one of claims 35 and 36, wherein the electrical property is a hole sheet resistance (R _H ) and the fifth relation (f ₁ ) represents an additional third resistance difference (ΔR _{AA ′} ). Further includes parameters,
The method comprises:
(d) applying an additional fifth potential across the first and fourth contact elements to generate an additional fifth current at the surface portion at the first location,
(e) measuring the additional fifth current through the first or fourth contact element, and
(f) measuring an additional fifth voltage across the second and third contact elements,
(g) calculating an additional fifth resistance value R _A based on the additional fifth current and the additional fifth voltage, or
(g ') a step of holding the fifth resistance (R _A) from the step of determining the distance to an additional fifth resistance (R _A), and
(h) applying an additional sixth potential across the second and third contact elements to generate an additional sixth current in the surface portion at the first location,
(i) measuring the additional sixth current through the second or third contact element,
(j) measuring an additional sixth voltage across the first and fourth contact elements, and
(k) calculating an additional sixth resistance value R _{A '} based on the additional sixth current and the additional sixth voltage, or
(k ') adding the distance to the fifth _'From the step of determining the value of the sixth resistance (R _A resistance value (R _A), comprising: holding a), and
(l) calculating the additional third resistance difference ΔR _{AA ′} based on the difference between the additional fifth resistance value and the additional sixth resistance value, or
(l '), characterized in that it comprises the step of holding the third resistance difference (△ R _AA') from the step of determining by said additional third resistance difference (△ R _AA the distance _") more. 44. The method of claim 43, wherein the fifth relational expression is

ΔR _{AA ′} represents the additional third resistance difference ΔR _{AA ′} , y represents the distance y or the additional distance, and a is the contact point of the first and second contact elements. The distance between them, b represents the distance between the contact points of the second and third contact elements, and c represents the distance between the contact points of the third and fourth contact elements. 38. A method according to any one of claims 35 to 37, wherein the electrical property is sheet resistance R ₀ and the fifth relation g represents pseudo sheet resistance R _P. Further comprising a seventeenth parameter,
The method comprises:
(d) applying an additional fifth potential across the first and fourth contact elements to generate an additional fifth current at the surface portion at the first location,
(e) measuring the additional fifth current through the first or fourth contact element,
(f) measuring an additional fifth voltage across the second and third contact elements,
(g) calculating an additional fifth resistance value R _A based on the additional fifth current and the additional fifth voltage, or
(g ') a step of holding the fifth resistance (R _A) from the step of determining the distance to an additional fifth resistance (R _A), and
(h) applying an additional sixth potential across the second and third contact elements to generate an additional sixth current in the surface portion at the first location,
(i) measuring the additional sixth current through the second or third contact element,
(j) measuring an additional sixth voltage across the first and fourth contact elements,
(k) calculating an additional sixth resistance value R _{A '} based on the additional sixth current and the additional sixth voltage, or
(k ') holding the sixth resistance value R _A' from determining the distance as an additional fifth resistance value R _{A '} , and
(l) a fifth resistance average of the additional fifth resistance value R _A and the additional sixth resistance value R _{A ′} (

),
(d ") applying an additional first potential across said first and third contact elements to generate an additional first current in said surface portion at said first location,
(e ") measuring said additional first current through said first or third contact element,
(f ") measuring an additional first voltage across said second and fourth contact elements,
(g ") calculating an additional first resistance value R _B based on said additional first current and said additional first voltage, or
(g ''') comprising: holding the first resistance value (R _B) from the step of determining the distance to the additional first resistance value (R _B), and
(h ") applying an additional second potential across said second and fourth contact elements to generate an additional second current in said surface portion at said first location,
(i ") measuring said additional second current through said second or fourth contact element,
(j ") measuring an additional second voltage across said first and third contact elements,
(k ″) calculating an additional second resistance value R _{B ′} based on the additional second current and the additional second voltage, or
(k ''') holding the second resistance value R _B' from determining the distance as an additional second resistance value R ' _B , and
(l ″) a sixth resistance average of the additional first resistance value R _B and the additional second resistance value R _{B ′} (

),
(m) the fifth resistance average (

), The sixth resistance average (

And a sixth relationship comprising the eighteenth, nineteenth, and twentieth parameters representing the pseudo sheet resistance R _P , respectively; and
(n) the fifth resistance average in the sixth equation (

) And the sixth resistance average (

) Determining the pseudo sheet resistance R _P using the eighteenth parameter and the nineteenth parameter, respectively. 46. The method of claim 44 or 45, wherein the sixth relation is

, Wherein R _P is the pseudo sheet resistance,

Is the first resistance average,

Is the second resistance average. An apparatus for determining a distance between a first location on an electrically conducting surface portion of a test sample and an electrical boundary of the electrically conductive surface portion,
Multi-point probe comprising a first contact element, a second contact element, a third contact element, and a fourth contact element, each contact element establishing an electrical contact with the test sample. Define a contact point for
The method according to any one of claims 1 to 34. A control unit configured to carry out a method of determining a distance or an additional distance
/ RTI > An apparatus for determining electrical properties at a first location on an electrically conducting surface portion of a test sample, the apparatus comprising:
Multi-point probe comprising a first contact element, a second contact element, a third contact element, and a fourth contact element, each contact element establishing an electrical contact with the test sample. Define a contact point for
47. A method of determining electrical properties at a first location on an electrically conductive surface of a test sample according to any one of claims 35 to 46. Configured control unit
/ RTI >

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